jmc

In the equation $\frac{12\star 2}{9\ast 3}=4$, the numerator of the fraction in the left hand side must be quadruple the denominator. By trial and error, the only way this works is if the $\star$ operation is multiplication and the $\ast$ operation is subtraction, in which case the equation becomes $\frac{12\cdot 2}{9-3}=\frac{24}{6}=4$. Thus, the value of the given expression is $\frac{10\cdot 7}{24-9}=\frac{70}{15}=\boxed{\frac{14}{3}}$.