To simplify the given expression $i^7 \left(\frac{12}{6i^3}\right)$, follow these steps:

1. Simplify the fraction $\frac{12}{6i^3}$: $\frac{12}{6i^3} = 2i^{-3}$

2. Now, multiply this result by $i^7$: $i^7 \cdot 2i^{-3}$

3. Combine the powers of $i$: $2i^{7 - 3} = 2i^4$

4. Recall the powers of $i$: $i^4 = (i^2)^2 = (-1)^2 = 1$

5. Substitute $i^4$ with 1: $2i^4 = 2 \cdot 1 = 2$

Therefore, the simplified expression is: $2$

Would you like more details or have any questions? Here are some related questions:

1. What are the properties of the imaginary unit $i$?
2. How do you simplify expressions involving imaginary numbers?
3. What are the steps to simplify complex fractions?
4. How do the powers of $i$ cycle?
5. What is the significance of $i^4 = 1$?
6. Can you provide examples of simplifying other expressions with imaginary numbers?
7. How can you verify the simplification of an expression involving $i$?
8. What are some common mistakes when working with powers of $i$?

Tip: Remember that $i$ cycles every four powers: $i, -1, -i, 1$.