smc

If two of the angles are $60^{\circ }$, then the other angle is $60^{\circ }$ because angles in triangle add up to $180^{\circ }$. That makes the triangle an equilateral triangle, so all sides are $4$ inches long. Using the area formula $A=\frac{s^2\sqrt{3}}{4}$, the area of the triangle is $\frac{4^2\sqrt{3}}{4}=4\sqrt{3}$ square inches, which is answer choice $\boxed{4\sqrt{3}}$.