To solve the equation 2.2^(2x) + 4^(2.4^x) = 1056, we can start by simplifying the equation.

Let's first simplify the term 4^(2.4^x):

4^(2.4^x) = (2^2)^(2.4^x) = 2^(2 * 2.4^x) = 2^(4.8^x)

Now, the equation becomes:

2.2^(2x) + 2^(4.8^x) = 1056

To further simplify the equation, we can rewrite 2.2 as 2 * 1.1:

(2 * 1.1)^(2x) + 2^(4.8^x) = 1056

Now, let's substitute y = 1.1^x:

(2 * y)^(2x) + 2^(4.8^x) = 1056

Using the property of exponents, we can rewrite the equation as:

2^(2x) * y^(2x) + 2^(4.8^x) = 1056

Now, let's rewrite 2^(4.8^x) as (2^4.8)^x:

2^(2x) * y^(2x) + (2^4.8)^x = 1056

Since (2^4.8)^x is a constant, let's substitute z = (2^4.8)^x:

2^(2x) * y^(2x) + z = 1056

Now, we have a quadratic equation in terms of 2^(2x):

(2^(2x))^2 + z * 2^(2x) - 1056 = 0

Let's substitute u = 2^(2x):

u^2 + z * u - 1056 = 0

Now, we can solve this quadratic equation for u using factoring, completing the square, or the quadratic formula.

Once we find the values of u, we can substitute back to find the values of x.