$$Compute $43_6 \cdot 51_6$ in base 6.$$
One way as follows:
In decimal: (4*6 + 3)*(5*6 + 1) = 837
Convert to base 6: 35136
(Though this might be considered to be a cheat if the workings are all supposed to be done in base 6!)
.
436
x 516
--------
43
343
------
35136