To solve the equation 2^9 * (x - 612) = 2^12, we can start by simplifying the equation using the properties of exponents.

First, we can rewrite 2^9 as 2^12 / 2^3, since 12 - 3 = 9.

So the equation becomes (2^12 / 2^3) * (x - 612) = 2^12.

Next, we can simplify further by canceling out the common factor of 2^3:

2^12 * (x - 612) / 2^3 = 2^12.

This simplifies to 2^9 * (x - 612) = 2^12.

Since the bases are the same (2), we can equate the exponents:

9 + log2(x - 612) = 12.

Subtracting 9 from both sides gives:

log2(x - 612) = 12 - 9.

log2(x - 612) = 3.

Now, we can rewrite the equation in exponential form:

2^3 = x - 612.

8 = x - 612.

Adding 612 to both sides gives:

x = 620.

Therefore, the solution to the equation 2^9 * (x - 612) = 2^12 is x = 620.