We are able to send faxes but are unable to receive them. How can we Fix this problem

Sounds like the scanner bulb is burnt out or it's not able to move the scanner sled.
It should be saying "scanner error" as well. (and I think you meant unable to scan, copy or send fax)
No fix unfortunately other than getting a replacement unit (which I believe now is the 8500 premiere)

If you need a replacement, your timing is good, they are $200 off right now, and selling for $299.

Your unit as it stands still makes a good printer and will receive faxes, and you CAN send a fax as long as you do it from the computer.

make sure there is no light burning next to manual or ans hook up!If there is one press the button till they all gone!

check your rx setting (receive) mode ?, fix it to auto mode

You probably have to set something up in your settings.

Usually this goes: Settings>Fax Setup>Receive

Of course, this is generic, and all Fax machines are different. Is there a model number?

I am unable to send or receive faxes I do not know whats the problem.

Per HP:

Definition

An error occurred during transmission after one or more partial pages were sent. The sending machine was unable to restart the control channel connection(handshake) before sending more data. This error typically occurs when the receiving fax disconnects after receiving part of a page. It can also be caused if the receiving fax is using a fax format incompatible with the HP fax (usually during color faxing).

Solution

Try the fax at a different time when telephone line conditions have improved.

You don't have the cable plugged into the "telephone" jack instead of the "line" jack on the machine do you?

Try calling your fax machine with a cell phone to see if the fax answers. If not, check that the phone wire to the fax is plugged into the LINE socket, NOT THE PHONE SOCKET on the fax machine. Next, go to the MENU on the fax.You may have to check or change one or more of the following settings by trial-and error to fix the problem. BEFORE YOU CHANGE ANY SETTING, WRITE DOWN OR PRINT OUT THE ORIGINAL SETTINGS. In the MENU, find FAX SETTINGS, FAX SET-UP, or INITIAL SETUP settings. Try changing one or more of the following: PULSE/TONE, RECEIVE MODE, SEND MODE, RING DELAY, RING TIME, OVERSEAS MODE, etc.

unable to send fax through power line carrier communication. only some part of the document received

here you might find an answer:

http://welcome.solutions.brother.com/bsc/public/us/us/en/faq/faq_top.htm?reg=us&c=us&lang=en&prod=mfc240c_all