Question: How do I show that picking 3 socks containing just black and red socks that I must get either a pair of black or red socks?

I mean it's fairly obvious, but how would I show it?

Is this pigeon hole?

Answer: 
Two holes: red and black........
You could show it by brute force, listing all $8$ of the possible outcomes of picking $3$ socks: BBB, BBR, BRB, RBB, BRR, RBR, RRB, and RRR. However, that’s a little messy, and the pigeonhole principle provides a neater answer. You have two pigeonholes, one labelled BLACK and the other labelled RED. You pull out $3$ socks and put each of them into the appropriate pigeonhole. Since there were more socks than pigeonholes, one pigeonhole must contain more than one sock.