1. **State the problem:** Solve the system of equations using the elimination method: $$3x + 2y = 6$$ $$x = 4$$ 2. **Substitute the known value:** Since $x = 4$, substitute $4$ for $x$ in the first equation: $$3(4) + 2y = 6$$ 3. **Simplify the equation:** $$12 + 2y = 6$$ 4. **Isolate $y$:** Subtract 12 from both sides: $$\cancel{12} + 2y - \cancel{12} = 6 - 12$$ $$2y = -6$$ 5. **Solve for $y$:** Divide both sides by 2: $$\frac{2y}{\cancel{2}} = \frac{-6}{\cancel{2}}$$ $$y = -3$$ 6. **Final answer:** $$x = 4, \quad y = -3$$