Design a 32x4 memory chip using 32x8 memory chip
Going from 32x8 to 32x4 is trivial, you just don't use half of it.

Making a 32x4 from a single 16x8 requires nibble write strobes. With only byte strobes you have to fall back on read-modify-write. But still not impossible!

Your teacher probably is frowning on wasting half the memory. Most school assignments are of the type "How do I build a AxB memory from CxD type" and always you find you need exactly a whole number of CxD blocks.

By the way: FPGAs often have 36 bits wide memory. Many a design only needs 8/16 or 32 bits and drop the last 4 bits. So practically dropping bits is done very, very regularly.