We are tasked with calculating the expression:

$\text{The square of } 2i \times \text{the square of } 6i.$

Step 1: Represent the expression mathematically

The given expression can be written as: $(2i)^2 \times (6i)^2$

Step 2: Simplify each square term

1. $(2i)^2 = 2^2 \cdot i^2 = 4 \cdot (-1) = -4$, since $i^2 = -1$.
2. $(6i)^2 = 6^2 \cdot i^2 = 36 \cdot (-1) = -36$.

Step 3: Multiply the results

Now, substitute back into the expression: $(2i)^2 \times (6i)^2 = (-4) \times (-36) = 144.$

Final Answer:

$\boxed{144}$

Would you like a deeper explanation or have further questions? Here are some related questions for further practice:

1. What is the result of $(3i)^3 \times (4i)^3$?
2. Simplify the expression $(5i)^4 \div (i^2)$.
3. How do you multiply and simplify $(1 + 2i) \times (3 - 4i)$?
4. What is the square of $(2 + 3i)$?
5. How do you represent a complex number in polar form?

Tip: Always remember $i^2 = -1$, which is key to simplifying expressions involving imaginary numbers.