Answer
$$ \dfrac {x^{2}}{4}-\dfrac {y^{2}}{32}=1$$
Work Step by Step
Equation of hyperbola with a format of
$$\dfrac {x^{2}}{a^{2}}-\dfrac {y^{2}}{b^{2}}=1\left( a > 0,b > 0\right) $$
Foci are $\left( \pm c,0\right) ;c^{2}=a^{2}+b^{2}$
Vertices are $\left( \pm a,0\right) $
Given vertices $(\pm2,0)$ we find $a=2$ and given foci $(\pm6)$ we find $c=6$
$\Rightarrow c^{2}=a^{2}+b^{2}\Rightarrow 6^{2}=2^{2}+b^{2}\Rightarrow b^2=32$
Then the equation will be
$$\Rightarrow \dfrac {x^{2}}{4}-\dfrac {y^{2}}{32}=1$$
