Find the standard form of the equation of the hyperbola with the given characteristics.
Foci: (0, ±8); asymptotes: y = ±2x
recall that
y^2/b^2 - x^2/a^2 = 1
has
c^2 = a^2 + b^2
asymptotes y = ±b/a x
so now you have
a^2 + b^2 = 84
b = 2a
Finish it off. Post your work if you get stuck.