1. **State the problem:** Expand the expression $$(3t - 4)(2t - 3)$$. 2. **Formula used:** Use the distributive property (FOIL method) for binomials: $$(a + b)(c + d) = ac + ad + bc + bd$$. 3. **Apply FOIL:** - First: $3t \times 2t = 6t^2$ - Outer: $3t \times (-3) = -9t$ - Inner: $-4 \times 2t = -8t$ - Last: $-4 \times (-3) = 12$ 4. **Combine like terms:** $$6t^2 - 9t - 8t + 12 = 6t^2 - 17t + 12$$ 5. **Final answer:** $$\boxed{6t^2 - 17t + 12}$$