#### Answer

$\frac{dx}{dt} = 3$

#### Work Step by Step

Given that $\frac{dy}{dt}$ = -2 and $2x+3y=12$
on differentiating y with respect to time
$\frac{d(2x+3y)}{dt}$ = $\frac{d 12}{dt}$
$\frac{d2x}{dt}+\frac{d3y}{dt}$ = $0$
so $2\frac{dx}{dt} + 3\frac{dy}{dt}$ = 0
$2\frac{dx}{dt} = -3 \times (-2)$
Thus, the answer is $\frac{dx}{dt} = 3$