Calculate the slope of the line passing through the points (3, 0) and (0, 2).

The formula for the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is $m = \frac{y_2 - y_1}{x_2 - x_1}$.
Let $(x_1, y_1) = (3, 0)$ and $(x_2, y_2) = (0, 2)$.

The equation of the second line is given as $y = ax - 3$. This equation is in the slope-intercept form $y = mx + c$, where $m$ is the slope.
So, the slope of the second line is $m_2 = a$.

Since the two lines are parallel, their slopes must be equal: $m_1 = m_2$.

Comparing this result with the given options, the correct answer is $-\frac{2}{3}$.