There are a couple of ways to solve. Convert both numbers to decimal and multiply; or use long multiplication in the base-3 system.
1 Convert to decimal: 2012 is 59 and 201 is 19. ab=1121, which must be converted back to basae 3. To convert back to base 3, there are several methods. Divide by 3: 373 rem 2, so 2 is the last digit. Divide 373 by 3: 124 rem 1, next to last digit is 1; 124/3=41 r 1, next digit is 1; 41/3=13 r 2; 13/3=4 r 1; 4/3=1 r 1 (11 is the start). So number is the remainders in reverse order: 1112112. To convert 2012 base 3 here's what you do: start on the left; 3*2+0 (the next digit)=6; 3*6+1=19; 3*19+2=59. 201 converts to: 2*3+0=6; 3*6+1=19.
2 Long multiplication:
......2012
......x201
-----------
......2012
11101
------------
1112112
------------
Note that 2*2=11 in base 3.
Let me know if you don't understand any of this by adding a comment.