The inequality \(|z + 2 - 3i| \leq 2\) represents a circle on the Argand diagram with center at \((-2, 3)\) and radius 2.

The inequality \(\text{arg} \, z \leq \frac{3}{4}\pi\) represents the region below the line with argument \(\frac{3}{4}\pi\), which is a half-line starting from the origin and making an angle of \(\frac{3}{4}\pi\) with the positive real axis.

To find the required region, shade the area inside the circle centered at \((-2, 3)\) with radius 2, and below the line \(\text{arg} \, z = \frac{3}{4}\pi\).