To solve this system of equations, we can use the method of substitution or elimination.

First, let's solve the first equation for x:

3x - 2y = 16
3x = 16 + 2y
x = (16 + 2y)/3

Now, substitute this expression for x into the second equation:

(16 + 2y)/3 + 4y = -4
16 + 2y + 12y = -12
14y = -28
y = -28/14
y = -2

Now, substitute y = -2 back into the first equation to solve for x:

3x - 2(-2) = 16
3x + 4 = 16
3x = 12
x = 4

Therefore, the solution to the system of equations is x = 4 and y = -2.