To solve this equation, we can first simplify the left side by combining like terms:

3^x + 2 + 4*3^x + 1 + 3^x - 1 = 6^6
8*3^x + 2 = 6^6

Now, we can rewrite 6^6 as (2*3)^6 = 2^6 * 3^6 = 64 * 729 = 46656.

So, the equation becomes:

8*3^x + 2 = 46656

Subtracting 2 from both sides:

8*3^x = 46654

Dividing by 8:

3^x = 5832

Now, we need to find the value of x that satisfies this equation. Since 5832 is equal to 3^8, we can rewrite the equation as:

3^x = 3^8

Therefore, x = 8.

So, the solution to the equation is x = 8.