1. **State the problem:** We are given two equations: $$\frac{x}{y} = 4$$ and $$x - y = 6$$ We need to find the value of $x + y$. 2. **Use the first equation to express $x$ in terms of $y$:** $$x = 4y$$ 3. **Substitute $x = 4y$ into the second equation:** $$4y - y = 6$$ 4. **Simplify the left side:** $$3y = 6$$ 5. **Solve for $y$:** $$y = \frac{6}{3}$$ Show cancellation: $$y = \frac{\cancel{6}}{\cancel{3}} = 2$$ 6. **Find $x$ using $x = 4y$:** $$x = 4 \times 2 = 8$$ 7. **Calculate $x + y$:** $$x + y = 8 + 2 = 10$$ **Final answer:** $$\boxed{10}$$