How do you set the number of rings before fax picks up?

There is excellent support here on basic fax setups. You have what is known as "Distinctive Ringing Service". There are pros and cons to the various setups. I assume you recognize the rings and answer only when the ring for the landline talk comes on. The fax will pick up the faxes, and the answering machine will pick up the voice.

Need model number of your fax - google that!

Service manual for your phone.

http://service.us.panasonic.com/OPERMANPDF/KXTG7841-MUL.PDF
This link shows various configurations of setting up your phone/fax/answering machine or using an answering service.
http://h10025.www1.hp.com/ewfrf/wc/document?cc=us&lc=en&docname=c00059780#Dist_ring
Distinctive Ringing Service setup While it is not available everywhere, a distinctive ringing service can be purchased from most telephone companies. With this service, more than one phone number is assigned to the same phone line. Each phone number will ring differently. The main number will ring with a normal single ring and the additional number will ring with a distinctive ring pattern assigned by the phone company.
When a distinctive ringing service is used, set the Rings to Answer to 2 and then follow the steps below to set the distinctive ringing pattern:

1. Press Setup , press 4 , and then press 1 to enter the Answer Ring Pattern setup of the Advanced Fax settings.
2. Use the Right Arrow to scroll through the available settings. When the ring pattern assigned by the phone company displays (double or triple rings), press OK .

For more details on how to setup your Lexmark X4650 printer for faxing, please refer to the User's Guide found on the Lexmark website.
Additional info:If you have an answering on the same line as your fax:

To make sure the printer picks up incoming faxes, set Auto Answer to On, and then set the printer to pick up after a greater number of rings than the answering machine. For example, if the answering machine picks up calls after four rings, then set the printer to pick up after six rings. This way, the answering machine picks up calls first and your voice calls are received. If the call is a fax, then the printer detects the fax signal on the line and takes over the call.

If you have a voicemail feature associated in the same line as your fax:

Voice mail and fax can share the same telephone line if you subscribe to a distinctive ring service offered by your telephone company. This feature allows you to have multiple telephone numbers on one telephone line. Each telephone number has a designated ring pattern (single ring, double ring, triple ring, or double and triple ring). The different ring patterns let you know which telephone number was dialed, and which device you should use to answer the call.

If you do not have distinctive ring service, then set the printer to receive faxes manually (Auto Answer Off). This setting lets you receive both voice calls and fax calls, but works best if you use voice mail more often. You need to turn off voice mail whenever you are expecting a fax.

If you have an answering machine connected to the same line as your fax:

To make sure the printer picks up incoming faxes, set Auto Answer to On, and then set the printer to pick up after a greater number of rings than the answering machine. For example, if the answering machine picks up calls after four rings, then set the printer to pick up after six rings. This way, the answering machine picks up calls first and your voice calls are received. If the call is a fax, then the printer detects the fax signal on the line and takes over the call.

If you have a voicemail feature associated to the same line as your fax:

Voice mail and fax can share the same telephone line if you subscribe to a distinctive ring service offered by your telephone company. This feature allows you to have multiple telephone numbers on one telephone line. Each telephone number has a designated ring pattern (single ring, double ring, triple ring, or double and triple ring). The different ring patterns let you know which telephone number was dialed, and which device you should use to answer the call.

If you do not have distinctive ring service, then set the printer to receive faxes manually (Auto Answer Off). This setting lets you receive both voice calls and fax calls, but works best if you use voice mail more often. You need to turn off voice mail whenever you are expecting a fax.

I hope this helps.

Should you need further assistance, please contact Lexmark Technical Support Center.

It seems that you're sharing your home phone line with your Lexmark fax machine. You can adjust the "pick-up" ring from the printer operator panel by pressing the Setup button > Fax Setup > Ringing and Answering > Pick Up On > select your preferred number of rings before the fax answers.
Please note:
If you have an answering machine connected to the same line as the fax, set the answering machine to answer incoming calls before the printer does. Increase the number of rings by a factor of 3 over the answering machine. For example, if the answering machine is set to pick up on 4 rings, set the printer to pick up on 7 rings.

If you have a voicemail feature in the same line as the fax, you may subscribe from your phone service provider for a distinctive ring pattern feature. You can program your printer to have a distinctive ring pattern and phone number for incoming faxes.

Should you still need assistance, please leave a comment to my response and I'll get back to you. Should this resolves your problem, your rating will be greatly appreciated.

Either your fax machine is set to answer on more rings then your answering machine is or you dont have the automatic answer key pushed?

Determine how many rings your answering machine picks up on and then change the number of rings to a lower amount on your fax machine. To change the number of rings before picking up the line, press the "menu" key on the fax machine and use the up and down arrows to scroll until you find the "basic fax set up" or the "advanced set up" areas. I am not sure which one will have the number of rings setting. Try looking in both until you find it.

when you see it press "ok" or "enter" get in and change the amount of rings before answering. call your fax machine to make sure it picks up before your answering machine.

This should solve your problem.

I have a HP Officejet J6480 All-In-One and needed the answering machine and fax to be on at the same time.  I called the help line at HP and they said I needed another phone line into the home but I tried this and it worked. 
First I got a different phone number for the fax machine - they do this for no charge at my phone company. This is not another physical line into the home - it is just another phone number with a different ring - it rings 2 fast rings for the fax machine instead of the phones regular one ring. I set the answering machine built into the phone to pick up after 4 rings and I set the fax machine to pick up on 2 rings. Be sure to set it so the fax pick up number of rings are less than the answering machine pick up number of rings.  It worked for me. Hope this works for you too.

Press
function
64
set

look at the printout
look for number of rings

to set the parameter
press
function 74
set

Hi,

Setting Ring Delay:
The Ring Delay setting determines the number of times the fax machine rings before it answers. If you have extension phones on the same line as the fax machine, keep the Ring Delay at a default setting of 4:
1 Press Function/Set, 2, 1.
2 Press < or > to select how many times the line rings before the fax machine answers (00 – 04) and press Function/Set. If you select 00, the line doesn’t ring at all.
3 Press Stop to exit.

Hope that's clear enough :)

Chris (ziraffa)

check the setting in the receive mode button. set it to fax

here is the manual

http://www.retrevo.com/s/sharp+UX-B700+manual

good luck