First, try to understand what is refinement.

A partition P1 is called a refinement of the partition P2 if every set in P1 is a subset of one of the sets in P2.

**S1: The partition of the set of bit strings of length 16 formed by equivalence classes of bit strings that agree on the last eight bits is a refinement of the partition formed from the equivalence classes of bit strings that agree on the last four bits**

Here in P1 for each distinct pattern of last 8 bits one partition is created. In P2 for each distinct pattern of last 4 bits one partition is created.

Every partition of P1 is a subset of some partition of P2, so P1 is refinement of P2.

In same way in S2 too P1 is refinement of P2.