A. Your PMF is not a function perse, in the sense you are thinking (perhaps) of it as. It is simply a chart with R and Y being as you say. To set this up you need to know the possible values of R and Y. You are told that you are choosing two socks without replacement, and so your values of R and Y can range from 0 to 2 (do you see why?)
You then set up a grid, but how you set up the grid is the important part. In this scenario, both the R and the Y are columns and they can take on values of 0, 1, 2 since we are selecting two socks. P(R=0) would be the probability you select no red socks, which means the probability that on the first and second draw you get a green or a yellow - (12/16)(11/16). P(R=1) means you got a red on the first or second draw - (8/16)(12/15)+(12/16)(8/15). And so on and so forth.
Once you set up your probability mass function, figuring out the rest should be easy (assuming you know how to figure out the rest).