1. **State the problem:** We need to find the value of $d$ in the equation $$\frac{x^{24}}{x^{d}} = x^{8}.$$\n\n2. **Recall the exponent division rule:** When dividing powers with the same base, subtract the exponents: $$\frac{x^{a}}{x^{b}} = x^{a-b}.$$\n\n3. **Apply the rule to the left side:** $$\frac{x^{24}}{x^{d}} = x^{24 - d}.$$\n\n4. **Set the exponents equal:** Since $$x^{24 - d} = x^{8},$$ the exponents must be equal: $$24 - d = 8.$$\n\n5. **Solve for $d$:** \n$$24 - d = 8$$\n$$\Rightarrow \cancel{24} - d = \cancel{8}$$\n$$24 - 8 = d$$\n$$16 = d.$$\n\n**Final answer:** $$d = 16.$$