1. **State the problem:** We need to show that for the function $g(x) = 2x$, the expression $g(x+3) - g(x-1)$ equals 8. 2. **Recall the function definition:** $g(x) = 2x$ means that for any input $x$, the output is twice $x$. 3. **Evaluate each term:** - Calculate $g(x+3)$ using the function: $$g(x+3) = 2(x+3) = 2x + 6$$ - Calculate $g(x-1)$ using the function: $$g(x-1) = 2(x-1) = 2x - 2$$ 4. **Form the expression:** $$g(x+3) - g(x-1) = (2x + 6) - (2x - 2)$$ 5. **Simplify the expression:** $$= 2x + 6 - 2x + 2$$ 6. **Cancel common terms:** $$= \cancel{2x} + 6 - \cancel{2x} + 2 = 6 + 2$$ 7. **Add the constants:** $$= 8$$ **Final answer:** $$g(x+3) - g(x-1) = 8$$ This shows the required result.