To solve for \( a \) in the equation
\[ \frac{2}{5}a = \frac{4}{15}, \]
we can start by isolating \( a \). We do this by multiplying both sides of the equation by the reciprocal of \( \frac{2}{5} \), which is \( \frac{5}{2} \):
\[ a = \frac{4}{15} \cdot \frac{5}{2}. \]
Now, let's perform the multiplication on the right side:
\[ a = \frac{4 \times 5}{15 \times 2} = \frac{20}{30}. \]
Next, we can simplify \( \frac{20}{30} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 10:
\[ a = \frac{20 \div 10}{30 \div 10} = \frac{2}{3}. \]
Thus, the solution for \( a \) is
\[ \boxed{\frac{2}{3}}. \]