To solve the problem in the image, we need to find the perimeter of the figure made of two rectangles in terms of $p$ and then simplify the expression.

Given:

• The figure is composed of two rectangles.
• The dimensions of the rectangles are given in terms of $p$:
  • Left Rectangle: $7p \times 7p$
  • Right Rectangle: $14p \times (7p + 8)$

Steps to Find the Perimeter:

1. Identify the lengths of all the sides of the figure:

   • The left side: $7p$
   • The right side: $14p$
   • The top side (combination of the top sides of both rectangles): $7p + 8$
   • The bottom side: $7p$ (from the left rectangle)
   • The middle side (from the bottom of the right rectangle to the top of the left rectangle): $8$

2. Add all the sides to find the perimeter:

   • The perimeter $P$ is the sum of all the outer sides: $P = 7p + 14p + (7p + 8) + 7p + 8 + 14p$

3. Simplify the expression:

   • Combine like terms: $P = (7p + 14p + 7p + 14p) + (8 + 8)$
   • Simplify further: $P = (7p + 7p + 14p + 14p) + 16 = 42p + 16$

Final Answer:

The perimeter of the figure in terms of $p$ is $\boxed{42p + 16}$.

Would you like any further details or explanations? Here are some related questions to consider:

1. What is the area of the entire figure in terms of $p$?
2. How would the perimeter change if the width of the second rectangle were doubled?
3. What if the height of the first rectangle were increased by a factor of 2?
4. If the height of the second rectangle were $14p - 5$, how would the perimeter change?
5. Can you express the area of the two rectangles separately in terms of $p$?
6. How would the problem change if both rectangles were squares?
7. What if you added another rectangle of width $7p$ and height $7p + 8$?
8. How would the perimeter be affected if the two rectangles were rearranged?

Tip: When finding the perimeter of a composite shape, it helps to carefully track each side's contribution to ensure no length is overlooked or double-counted.