To solve the expression \( 225 - 4 \cdot 10 \cdot (-3 \frac{2}{5}) \), we will first convert the mixed number into an improper fraction.
The mixed number \(-3 \frac{2}{5}\) can be converted as follows:
\[ -3 \frac{2}{5} = -\left(3 \cdot 5 + 2\right)/5 = -\frac{15 + 2}{5} = -\frac{17}{5} \]
Now substitute this back into the expression:
\[ 225 - 4 \cdot 10 \cdot \left(-\frac{17}{5}\right) \]
Calculating \(4 \cdot 10\):
\[ 4 \cdot 10 = 40 \]
Now, substitute this back:
\[ 225 - 40 \cdot \left(-\frac{17}{5}\right) \]
Calculate \(40 \cdot -\frac{17}{5}\):
\[ 40 \cdot -\frac{17}{5} = -\frac{40 \cdot 17}{5} = -\frac{680}{5} = -136 \]
Now substitute this back into the expression:
\[ 225 - (-136) = 225 + 136 \]
Now, perform the addition:
\[ 225 + 136 = 361 \]
Therefore, the final answer is:
\[ \boxed{361} \]