1. **State the problem:** Solve the equation $6u - 28 = 4(u - 6)$.\n\n2. **Apply the distributive property:** Expand the right side: $4(u - 6) = 4u - 24$. So the equation becomes:\n$$6u - 28 = 4u - 24$$\n\n3. **Isolate variable terms on one side:** Subtract $4u$ from both sides:\n$$6u - \cancel{4u} - 28 = \cancel{4u} - 24$$\nwhich simplifies to\n$$2u - 28 = -24$$\n\n4. **Isolate the constant term:** Add 28 to both sides:\n$$2u - 28 + 28 = -24 + 28$$\nwhich simplifies to\n$$2u = 4$$\n\n5. **Solve for $u$:** Divide both sides by 2:\n$$\frac{2u}{\cancel{2}} = \frac{4}{\cancel{2}}$$\nwhich simplifies to\n$$u = 2$$\n\n**Final answer:** $u = 2$