1. **State the problem:** We are given that one number is 4 more than another number. Let the smaller number be $x$ and the larger number be $y$. We know: $$y = x + 4$$ 2. **Given equation:** When three times the smaller number is added to twice the larger number, the result is 43: $$3x + 2y = 43$$ 3. **Substitute $y$ from step 1 into the equation:** $$3x + 2(x + 4) = 43$$ 4. **Simplify the equation:** $$3x + 2x + 8 = 43$$ $$5x + 8 = 43$$ 5. **Isolate $x$:** $$5x = 43 - 8$$ $$5x = 35$$ 6. **Solve for $x$:** $$x = \frac{35}{5}$$ $$x = 7$$ 7. **Find $y$ using $y = x + 4$:** $$y = 7 + 4 = 11$$ **Answer:** The smaller number is 7 and the larger number is 11.