Step 1: List the 8051's registers by their width.
The 8051 has a mix of 8-bit and 16-bit registers. The accumulator A, register B, the Program Status Word PSW, and the Stack Pointer SP are all only 8 bits wide.
Step 2: Pick out the ones that are 16 bits wide.
Only two registers in the 8051 need the full 16-bit width, the Program Counter, because it must be able to address the entire 64 KB program memory space, and the Data Pointer DPTR, because it is used to point anywhere within the same 64 KB external data or code space.
Step 3: Count them up.
That gives exactly two 16-bit registers in total.
\[ \boxed{2} \]