how many solutions does −3y+8=8−3y have?

Answer 1

To elaborate a bit to Raymond's correct answer, we can see that if we attempt to solve for y we will get to y = y, which has infinite solutions. A variable will always be equal to itself.

−3y+8=8−3y

*subtract 8 from both sides*

-3y = -3y

*divide by -3 to get y*

y = y

Answer 2

an infinite number of solutions

y = any real number, or any complex number

the equation is an identity, a tautology, always true regardless of the value of y