To solve the equation \( |x - 2| + 3 = -2 \), we start by isolating the absolute value:

1. Subtract 3 from both sides:
\[
|x - 2| = -2 - 3
\]
\[
|x - 2| = -5
\]

Since the absolute value cannot equal a negative number, this equation has no solution. Thus, there are no values of \( x \) that satisfy the original equation.