To solve this equation, we can simplify it by first combining the two square roots.

√2^x * √3^x = 216

√(2^x * 3^x) = 216

Now, we can simplify the expression inside the square root by using properties of exponents. Since both 2 and 3 are prime numbers, we can rewrite them as powers of themselves.

2^x 3^x = (2 3)^x

2^x * 3^x = 6^x

Now our equation becomes:

√6^x = 216

Taking the square root of both sides:

6^x = 216^2

6^x = 46656

Next, we can rewrite 46656 as a power of 6:

6^x = 6^6

Since the bases are the same, we can set the exponents equal to each other:

x = 6

Therefore, the solution to the equation is x = 6.