Slope intercept form: y=mx+b, with m being the slope and b being the y-intercept.
Plug 4 in for the slope, as that's given in the question:
y=4x+b
Now, we need to solve for the y-intercept, because the answer could be B, C, or D. You can do this by plugging in the given coordinate (-1,8) for x and y in the equation respectively.
8=4(-1)+b
Multiply.
8=-4+b
Add four to both sides.
12=b
The y-intercept is 12. Plug 12 into the equation for b:
y=4x+12 is the completed equation.
The answer is C.
I hope this helps :)