Let's denote Cassidy's younger brother's height as \( x \) inches. According to the information provided, we can write the relationship between their heights as follows:
Cassandra's height, which is 63 inches, is 6 inches less than 3 times her brother's height. This can be expressed with the equation:
\[ 63 = 3x - 6 \]
To write this equation in the form \( px + q = r \), we can rearrange it:
\[ 3x - 6 = 63 \]
In this form, \( p = 3 \), \( q = -6 \), and \( r = 63 \).
So, the equation in the specified form is:
\[ 3x - 6 = 63 \]