Here is a solution that uses only "elementary" operations (addition, subtraction, multiplication, and division).

$8 \div (3 - (8 \div 3))$ (or alternatively $\frac{8}{3 - \frac{8}{3}}$)
$= 8 \div \frac{1}{3}$
$= 24$

Here is a solution that uses only "elementary" operations (addition, subtraction, multiplication, and division).

$8 \div (3 - (8 \div 3))$ (or alternatively $\frac{8}{3 - \frac{8}{3}}$)
$= 8 \div \frac{1}{3}$
$= 24$

If we allow square roots, a simpler solution is possible.

$\sqrt{8 \times 8 \times 3 \times 3}$
$= 8 \times 3$
$= 24$

In fact, there are many more solutions if you allow more operations.