There are quite some posts in here that cite books and web sites useful for learning whatever language you want - try the search function. Did you look into the FAQ section? For exercises, pick any number of threads / posts in here, analyse and understand the problem and the solutions proposed, and try to compose a solution on your own.
Depending on your OS and shell versions, there might be very apt date commands or shell functions / builtins that lend themselves to solve your birthday problem, e.g. by translating both dates to epoch seconds, and then subtract them.