1. **State the problem:** Make $k$ the subject of the equation $$\frac{3k}{2} + \frac{h - 8k}{6} = a.$$\n\n2. **Combine the terms with $k$:** To combine the fractions, find a common denominator, which is 6. Rewrite each term:\n$$\frac{3k}{2} = \frac{3k \times 3}{2 \times 3} = \frac{9k}{6}.$$\nSo the equation becomes:\n$$\frac{9k}{6} + \frac{h - 8k}{6} = a.$$\n\n3. **Add the fractions on the left side:** Since denominators are the same, add numerators:\n$$\frac{9k + h - 8k}{6} = a.$$\nSimplify numerator:\n$$\frac{(9k - 8k) + h}{6} = a \Rightarrow \frac{k + h}{6} = a.$$\n\n4. **Isolate $k$:** Multiply both sides by 6 to eliminate the denominator:\n$$\cancel{6} \times \frac{k + h}{\cancel{6}} = 6a \Rightarrow k + h = 6a.$$\n\n5. **Solve for $k$:** Subtract $h$ from both sides:\n$$k + h - h = 6a - h \Rightarrow k = 6a - h.$$\n\n**Final answer:** $$k = 6a - h.$$