To solve the equation \( 6^{x+2} = 3 \times 6^x + 1188 \), we can start by rewriting \( 6^{x+2} \) as follows:

\[
6^{x+2} = 6^x \cdot 6^2 = 6^x \cdot 36
\]

Now, substituting this back into the equation gives:

\[
36 \cdot 6^x = 3 \cdot 6^x + 1188
\]

Next, we can move all terms involving \( 6^x \) to one side of the equation:

\[
36 \cdot 6^x - 3 \cdot 6^x = 1188
\]

This simplifies to:

\[
(36 - 3) \cdot 6^x = 1188
\]

\[
33 \cdot 6^x = 1188
\]

Now, we can divide both sides by 33:

\[
6^x = \frac{1188}{33}
\]

Calculating the right side gives:

\[
6^x = 36
\]

Since \( 36 \) can be expressed as \( 6^2 \), we have:

\[
6^x = 6^2
\]

Equating the exponents gives:

\[
x = 2
\]

Therefore, the solution to the equation is:

\[
\boxed{2}
\]