there are 26 socks in total (16 + 4 + 6)
so we are asked if if he pulls out a black OR white sock. the or should signal to you that you add these probabilities 16/26+6/26=22/26
now, it says that he puts it back in (in math terms, he replaces it) and then picks out a brown sock 4/26 now we just multiply those two probabilities together. the key word you want to look for is AND. and implies that you multiply the probabilites
22/26∗4/26=22/13∗1/13=22/169