The given points are: (-2,4) and (6,b)
The slope is -3/2
The slope is the change in Y over the change in x.
So you get: -3/2 = (b - 4) / (6 - -2)
Simplify to get: -3/2 = (b - 4) / 8
Now we see the denominator on the right is 8 and on the left is 2, this is a scale of 4: (8 / 2 = 4) so the numerator on the right needs to be scaled by 4 as well.
The left side is -3, so the right side needs to equal -3 x 4 = -12
Now we know b - 4 = -12, solve for b:
b -4 = -12, add 4 to both sides:
b = -8
Now check:
(-2,4) (6,-8)
Slope = (-8 - 4) / (6 - -2) = -12 /8 = -3/2
b = -8