1. **State the problem:** Simplify the expression $$\frac{6h^{5} \times 4h^{3}}{8h^{15}}$$. 2. **Use the laws of exponents and multiplication:** When multiplying terms with the same base, add the exponents: $$h^{a} \times h^{b} = h^{a+b}$$. 3. **Multiply the numerators:** $$6h^{5} \times 4h^{3} = (6 \times 4)(h^{5} \times h^{3}) = 24h^{8}$$. 4. **Rewrite the expression:** $$\frac{24h^{8}}{8h^{15}}$$. 5. **Simplify the fraction by dividing coefficients:** $$\frac{24}{8} = \cancel{\frac{24}{8}} = 3$$. 6. **Simplify the powers of $h$ by subtracting exponents:** $$\frac{h^{8}}{h^{15}} = h^{8-15} = h^{-7}$$. 7. **Combine the simplified parts:** $$3h^{-7}$$. 8. **Express with positive exponent:** $$3h^{-7} = \frac{3}{h^{7}}$$. **Final answer:** $$\frac{3}{h^{7}}$$.