To find the height \( h \) of the right rectangular prism with a square base, we can use the formula for the volume of a prism:
\[ V = A \times h \]
where \( V \) is the volume, \( A \) is the area of the base, and \( h \) is the height. Since the base is a square, if the side length of the square base is \( s \), then:
\[ A = s^2 \]
Given that the volume \( V = 192 \) cubic units, we have:
\[ 192 = s^2 \times h \]
From the image description, it is mentioned that the side length of the base is \( 4 \) units. Therefore, we can calculate the area of the base:
\[ A = 4^2 = 16 \text{ square units} \]
Now, substituting the area back into the volume equation:
\[ 192 = 16 \times h \]
To solve for \( h \), we divide both sides by \( 16 \):
\[ h = \frac{192}{16} = 12 \text{ units} \]
Therefore, the height \( h \) of the prism is \( \boxed{12} \) units.