To solve the equation \( 3^{(x - 2)} = 81 \), we first express 81 as a power of 3.
We know that:
\[ 81 = 3^4 \]
Now we can rewrite the equation:
\[ 3^{(x - 2)} = 3^4 \]
Since the bases are the same, we can set the exponents equal to each other:
\[ x - 2 = 4 \]
Now, solve for \( x \):
\[ x = 4 + 2 = 6 \]
Therefore, the solution is:
\[ \boxed{6} \]