Answer
$156 + 24\sqrt10$
Work Step by Step
In order to do this, we add up the surface areas of the sides. Thus, we first add the three sides of known lengths:
$ SA = 2\times(6)\times(8) \times(6) \times (1/2) +6(12)=156$
We now find the length of the missing side:
$ l = \sqrt{6^2+2^2}= \sqrt{40}$
Using this, we add the lengths of the unknown surface areas:
$SA= 156 + \sqrt{40}(12) = $$156 + 24\sqrt10$