Algebra

y=3x+12    Solve for 'x'

(y-12)/3 = x       then switch the 'x' and 'y's

(x-12)/3 = y

or    y = 1/3 x -4

Flip the x and the y, so it becomes $x=3y+12$

Then just solve for y

$x-12=3y+12-12$

$\frac{x-12}{3}=\frac{3y}{3}$

$\frac{x}3-4=y$

So the inverse is $\frac{x}3-4=y$