1. **State the problem:** Simplify the expression $3(4t+3s) - 5(t-2s)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside. $$3(4t+3s) = 3 \times 4t + 3 \times 3s = 12t + 9s$$ $$-5(t-2s) = -5 \times t + (-5) \times (-2s) = -5t + 10s$$ 3. **Combine the results:** $$12t + 9s - 5t + 10s$$ 4. **Group like terms:** $$ (12t - 5t) + (9s + 10s)$$ 5. **Simplify each group:** $$ 7t + 19s$$ 6. **Final answer:** $$\boxed{7t + 19s}$$