The question reads:

Use synthetic division to find P(2) for P(x) = x^4 - 8x^3 - 8x^2 - 10x - 2

I have no idea how to do this problem. Could someone give me a step by step explanation or link me to somewhere I can find out how?

this page (youtube) not only shows how to do synthetic division, but the last third of the clip gets right to your type of problem.

http://www.jiskha.com/display.cgi?id=1242777110

your synthetic division setup would look like this

2 │ 1 -8 -8 -10 -2

see if you can come up with P(2) = -102