The vertex form of the equation of a parabola is x=8(y-1)^2-15. What is the standard form of the equation?

x = 8(y-1)^2 - 15

Standard form looks like this, x^2 -6x + 8, or y^2 - 6y + 8
To convert your equation into standard form all we have to do is expand it fully:
x = 8(y-1)^2 - 15
x = 8(y-1)(y-1) - 15
x = 8(y^2 -2y + 1) - 15
x = 8y^2 -16y + 8 - 15
x = 8y^2 -16y - 7