1. **State the problem:** Solve the equation $(x - y) + 3i = 4 + yi$ for real numbers $x$ and $y$. 2. **Recall the rule:** For two complex numbers to be equal, their real parts must be equal and their imaginary parts must be equal. 3. **Set real parts equal:** $$x - y = 4$$ 4. **Set imaginary parts equal:** $$3 = y$$ 5. **Substitute $y = 3$ into the real part equation:** $$x - 3 = 4$$ 6. **Solve for $x$:** $$x = 4 + 3 = 7$$ **Final answer:** $$x = 7, \quad y = 3$$