For what values of c,the linear equation 2x+cy-8 has equal values of x and y as it's solution?

An equation has an equal sign. 2x + cy - 8 = 0

One equation with three unknowns has no solution. Even when you set x=y you still have one equation with two unknowns. You need the number of equations equal to the number of unknowns to have a solution.

y = -2x/c + 8/c If c=2 or -2 then all points on the line will have x=y.