1. **State the problem:** Calculate the product $$(-3 \cdot 10^{4}) \cdot (2 \cdot 10^{-3})$$. 2. **Recall the multiplication rule for powers of 10:** When multiplying powers of 10, add the exponents: $$10^{a} \cdot 10^{b} = 10^{a+b}$$. 3. **Multiply the coefficients:** $$-3 \times 2 = -6$$. 4. **Add the exponents:** $$10^{4} \times 10^{-3} = 10^{4 + (-3)} = 10^{1}$$. 5. **Combine the results:** $$-6 \times 10^{1} = -6 \times 10 = -60$$. **Final answer:** $$-60$$.