Multiply :
4a and 6a + 7

Answer

To solve the problem of multiplying \( 4a \) and \( 6a + 7 \), we can follow these steps:

### Step 1: Write the expression for multiplication
We need to multiply \( 4a \) by the entire expression \( (6a + 7) \). This can be written as:
\[ 4a \times (6a + 7) \]

### Step 2: Apply the distributive property
Using the distributive property, we will multiply \( 4a \) by each term inside the parentheses:
\[ 4a \times 6a + 4a \times 7 \]

### Step 3: Multiply \( 4a \) by \( 6a \)
Now, we will multiply \( 4a \) by \( 6a \):
\[ 4a \times 6a = 24a^2 \]
Here, \( 4 \times 6 = 24 \) and \( a \times a = a^2 \).

### Step 4: Multiply \( 4a \) by \( 7 \)
Next, we multiply \( 4a \) by \( 7 \):
\[ 4a \times 7 = 28a \]
Here, \( 4 \times 7 = 28 \) and we keep the \( a \) as it is.

### Step 5: Combine the results
Now we can combine the results from Step 3 and Step 4:
\[ 24a^2 + 28a \]

### Final Answer
Thus, the final answer for the multiplication of \( 4a \) and \( 6a + 7 \) is:
\[ \boxed{24a^2 + 28a} \]

---