1. The problem states: Given that $$\int_3^7 f(x) \, dx = 12$$, find $$\int_3^7 2f(x) \, dx$$. 2. Recall the property of definite integrals: $$\int_a^b c \cdot f(x) \, dx = c \cdot \int_a^b f(x) \, dx$$ where $$c$$ is a constant. 3. Applying this property with $$c=2$$, we have: $$\int_3^7 2f(x) \, dx = 2 \cdot \int_3^7 f(x) \, dx$$ 4. Substitute the given value: $$= 2 \cdot 12 = 24$$ 5. Therefore, the value of $$\int_3^7 2f(x) \, dx$$ is $$24$$.