Use the area model to multiply 6(6c + 8), showing partial products and the final product.

We are asked to use the area model to multiply $ 6(6c + 8) $. Let's go step by step.

---

Step 1: Understand the Area Model

The area model breaks multiplication into parts. We have:

- A rectangle with length $ 6c + 8 $
- Width = 6

This rectangle is split into two smaller rectangles:
- One with dimensions $ 6 \times 6c $
- One with dimensions $ 6 \times 8 $

We calculate the partial products (areas of each smaller rectangle).

---

Step 2: Find the Partial Products

#### First rectangle (orange):
- Length: $ 6c $
- Width: $ 6 $
- Area: $ 6 \times 6c = 36c $

So, the first box should be filled with: $ 36c $

#### Second rectangle (pink):
- Length: $ 8 $
- Width: $ 6 $
- Area: $ 6 \times 8 = 48 $

So, the second box should be filled with: $ 48 $

---

Step 3: Write the Product

Now, add the partial products:

$$
6(6c + 8) = 36c + 48
$$

---

✔ Final Answer:

Partial products:
- Orange box: $ 36c $
- Pink box: $ 48 $

Product:
$$
6(6c + 8) = \boxed{36c + 48}
$$