If the volume of a cube is 12.167 cubic inches, what is the length of a side of the square?

What square?  I must assume you mean any of the 6 sides of the cube.

Volume of a cube of side length s is V = s^3.  Thus, 12.167 in^3 = s^3, and s = 2.3 in.

The length of one side of the cube is 2.3 in.  Equivalently, the length of one side of the square base of the cube is 2.3 in.

look at the picture.

y-intercept for the function on a picture is 4 → point (0, 4).

y-intercept for the function

is for x = 0. substitute:

y-intercept is 8 → point (0, 8).