The area of a triangle is $A = \frac{1}{2}bh$, and the height is $\frac{2}{3}$ of the base: $h = \frac{2}{3}b$.

$12 = \frac{1}{2} \cdot b \cdot \frac{2}{3}b = \frac{1}{3}b^2$

$b^2 = 36$

$b = 6$