How do you factor by grouping 3ab - b - 4 + 12a?

$3 a b - b - 4 + 12 a = \left(3 a - 1\right) \left(b + 4\right)$
Reorder as $3 a b - b + 12 a - 4$
This is $b \left(3 a - 1\right) + 4 \left(3 a - 1\right)$
Which is $\left(3 a - 1\right) \left(b + 4\right)$