I need to reset the number of rings before the 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.

Set the fax machine to Manual Receive. Set your answering machine to 4 or 5 rings. When the phone rings, pick it up, if you hear the chirping of a sending fax machine, press the Start Key on the fax and then hang up. The two faxes will communicate and you will receive your fax.

Change the answer machine rings to answer number to less than the fax number of rings to answer or increase the number of rings to answer on the fax machine. Would need exact model number of phone system to give more detail on programming steps. Info should be in manuals of phone system and fax machine.

reset your telephone line tone may be its select pulse

Set the FAX/MFC to MANUAL mode.
2 Press Menu/Set, 2, 0, 1.
3 Press to select DISTINCTIVE:SET?, and then press Menu/Set.
4 Press to select the prestored ring pattern you want to assign, and then press
Menu/Set. (You will hear each pattern as you scoll through the four patterns.)
Be sure to choose the pattern assigned by the telephone company.
5 Press Stop/Exit.

It means that your fax machine is "answering" the incoming call before you pick up the handset. Usually, the factory setting on the fax machine picks up after two incoming rings. There are three ways you can address this issue: 1.) You can either change the number of rings to, say, five incoming rings to give you enough time to answer the phone before the fax machine picks up, or 2,) you can find out if your fax machine has a feature that allows for the voice hook "click over" that will allow you to override the fax when you pick up your handset, or 3.) turn your fax machine off until you need to send a fax.

If you want to investigate number 2.), then you'll need your operator's manual.

Good luck.

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.

here is the manual

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

good luck