Let's solve \((7\frac{1}{4} - 6\frac{1}{4}) \times \left(\frac{2}{5} + \frac{3}{15}\right)\):

1. Subtract the Mixed Numbers:

Convert \(7\frac{1}{4}\) and \(6\frac{1}{4}\) to improper fractions:
\[
7\frac{1}{4} = \frac{29}{4}
\]
\[
6\frac{1}{4} = \frac{25}{4}
\]
Subtract these:
\[
\frac{29}{4} - \frac{25}{4} = \frac{4}{4} = 1
\]

2. Add the Fractions:

Add \(\frac{2}{5}\) and \(\frac{3}{15}\):
Convert \(\frac{3}{15}\) to \(\frac{1}{5}\) by simplifying:
\[
\frac{3}{15} = \frac{1}{5}
\]
Add \(\frac{2}{5}\) and \(\frac{1}{5}\):
\[
\frac{2}{5} + \frac{1}{5} = \frac{3}{5}
\]

3. Multiply the Results:

Multiply \(1\) by \(\frac{3}{5}\):
\[
1 \times \frac{3}{5} = \frac{3}{5}
\]

The result is:

B. \(\frac{3}{5}\)