parallel to $2 x-3 y+7=0$ and with the same $y$-intercept as $5 x-3 y-12=0$

Step 1 ：First, we find the slope of the given line $2x - 3y + 7 = 0$. We can rewrite it as $y = \frac{2}{3}x + \frac{7}{3}$, so the slope is $\frac{2}{3}$.

Step 2 ：Since the line we want to find is parallel to the given line, it will have the same slope, which is $\frac{2}{3}$.

Step 3 ：Next, we find the $y$-intercept of the line $5x - 3y - 12 = 0$. We can rewrite it as $y = \frac{5}{3}x - 4$. So, the $y$-intercept is $-4$.

Step 4 ：Using the slope and $y$-intercept, we can write the equation of the line we want to find as $y = \frac{2}{3}x - 4$.

Step 5 ：Thus, the equation of the line parallel to $2x - 3y + 7 = 0$ and with the same $y$-intercept as $5x - 3y - 12 = 0$ is \(\boxed{y = \frac{2}{3}x - 4}\).