left side = take k object from n objects, but 2 particular objects can't be both left out. It is (n.k)-(n-2,k-2), where (n-2,k-2) is number of ways that both of the particular 2 object are left out.

the right hand side we can pick up k-2 object from n-2 object then add those 2 objects to make k objects, or we can pick up k-1 objects from n-2 objects and pick up 1 object from the 2 particular object. It is (n-2, k-2) +2*(n-2,k-1).