To model the problem, the perimeter \( p \) of a square frame can be expressed with the equation:
\[ p = 4 \times s \]
where \( s \) represents the length of one side of the frame. For Stanley's frame, \( s \) is 8 inches. Therefore, we can substitute:
\[ p = 4 \times 8 \]
Now, let's calculate the perimeter:
\[ p = 32 \text{ inches} \]
Thus, the equation that models the problem is \( p = 4 \times 8 \), and the perimeter of the picture frame is 32 inches.