The size of a multiplexer is decide based on the number of data inputs it needs to handle.It is given in the question that there are 16 registers each of size 32 bits and in a common bus system using multiplexers, each multiplexer takes one input from every register. So, to take one input form 32 registers, we need 32 multiplexers to select each single input from the given 16 registers of size 32 bits each.
I hope this clears up your doubt.