1. **State the problem:** Simplify the expression $3x - y + 8 + x + y - 2$. 2. **Combine like terms:** Group the terms with $x$, the terms with $y$, and the constant terms separately. 3. The terms with $x$ are $3x$ and $x$, so add them: $$3x + x = 4x$$ 4. The terms with $y$ are $-y$ and $+y$, so add them: $$-y + y = 0$$ 5. The constant terms are $8$ and $-2$, so add them: $$8 - 2 = 6$$ 6. **Write the simplified expression:** $$4x + 0 + 6 = 4x + 6$$ 7. **Final answer:** $$\boxed{4x + 6}$$