I think the program as posted is buggy.
I think the following program is correct.

Am I close?

-- Russ

Quiz:
   mov   b,#16
   mul   ab
   rlc   a
   jb    p,Quiz1
   jz    Quiz2
   mov   a,#2
   sjmp  Quiz2
Quiz1:
   addc  a,#22h
   jc    Quiz2
   anl   a,#03h
   dec   a
Quiz2:
   addc  a,#0
   xch   a,b
   push  b              ; <------ add
   mov   b,#16          ; <------ add
   mul   ab             ; <------ add
   rlc   a
   jb    p,Quiz3
   jz    Quiz4
   mov   a,#2
   sjmp  Quiz4
Quiz3:
   addc  a,#22h
   jc    Quiz4
   anl   a,#03h
   dec   a
Quiz4:
   pop   b              ; <------ add
   addc  a,b
   ret