how do you solve the equation... 8y=3x+7?

Usually one would need two equations for one to get two unknowns.
Please , try and give us another equation.

He did: 8y=3x 7 for y

unfortunately it's not written as two.
8y=3x
y=7

Solve for x.

Way too trivial.

I think the original question was making 'y' the sbject of formula.

Thus, 8y = 3x + 7, then y = (3x+7)/8

If you want to know the main facts of this linear equation, use the distributive property (division) to get:
y=(3/8)x+7/8
so
the slope is 3/8 and the y intercept is 7/8
(mx+b)