$\\frac{1}{3}(x + 6) = \\frac{1}{2}(x - 3)$

$\frac{1}{3}(x + 6) = \frac{1}{2}(x - 3)$

$$6\times\frac{1}{3}(x+6) = 6\times\frac{1}{2}(x-3)$$
Simplify to get: $2(x+6) = 3(x-3)$

$$2x + 12 = 3x - 9$$

Subtract $2x$ from both sides:
$$12 = x - 9$$

Add 9 to both sides:
$$x = 12 + 9$$

$x=21$