1. **State the problem:** Find the value of $a$ in the equation $$\frac{a}{6} - \frac{3}{8} = \frac{11}{24}.$$\n\n2. **Use the formula:** To solve for $a$, isolate $a$ by adding $\frac{3}{8}$ to both sides:\n$$\frac{a}{6} = \frac{11}{24} + \frac{3}{8}.$$\n\n3. **Find a common denominator:** The denominators are 24 and 8. The least common denominator is 24. Convert $\frac{3}{8}$ to $\frac{9}{24}$:\n$$\frac{a}{6} = \frac{11}{24} + \frac{9}{24} = \frac{20}{24}.$$\n\n4. **Simplify the fraction:**\n$$\frac{20}{24} = \frac{5}{6}$$\n\n5. **Solve for $a$:** Multiply both sides by 6 to isolate $a$:\n$$a = 6 \times \frac{5}{6}.$$\nShow canceling common factors:\n$$a = \cancel{6} \times \frac{5}{\cancel{6}} = 5.$$\n\n6. **Final answer:**\n$$\boxed{5}.$$