1. Solve the equation: $$4a + 9a - 6a = 42$$ 2. Combine like terms on the left side: $$4a + 9a - 6a = (4 + 9 - 6)a = 7a$$ 3. The equation becomes: $$7a = 42$$ 4. To isolate $a$, divide both sides by 7: $$a = \frac{42}{7}$$ 5. Show the cancellation: $$a = \frac{\cancel{42}}{\cancel{7}} = 6$$ 6. Therefore, the solution is: $$a = 6$$ 7. Check the solution by substituting $a=6$ back into the original equation: $$4(6) + 9(6) - 6(6) = 24 + 54 - 36 = 42$$ 8. Since the left side equals the right side, the solution is correct.