**Solution:**

To find the greatest 3-digit number formed using the digits 7, 8, and 4, we need to arrange these digits in descending order.

The greatest 3-digit number is 874.

To find the number Q formed by reversing the digits of P, we need to reverse the order of the digits in P.

The number Q is 478.

a) To find P-Q, we subtract Q from P.

P-Q = 874 - 478 = 396

b) To check if P-Q is divisible by 3, we need to check if the sum of the digits in P-Q is divisible by 3.

The sum of the digits in 396 is 3+9+6 = 18.

Since 18 is divisible by 3, P-Q is also divisible by 3.

Therefore, P-Q is divisible by 3.

Explanation:

1. **Finding the greatest 3-digit number formed by using the digits 7, 8, and 4:**

To find the greatest 3-digit number, we need to arrange the digits in descending order.

The digits given are 7, 8, and 4.

Arranging them in descending order, we get the number 874.

So, the greatest 3-digit number formed using the digits 7, 8, and 4 is 874.

2. **Finding the number Q formed by reversing the digits of P:**

To find the number Q, we need to reverse the order of the digits in P.

The number P is 874.

Reversing the digits, we get the number Q as 478.

3. **Finding P-Q:**

To find P-Q, we subtract Q from P.

P-Q = 874 - 478 = 396.

So, P-Q is 396.

4. **Checking if P-Q is divisible by 3:**

To check if P-Q is divisible by 3, we need to find the sum of the digits in P-Q.

The digits in P-Q are 3, 9, and 6.

Sum of the digits = 3 + 9 + 6 = 18.

Since 18 is divisible by 3, P-Q is also divisible by 3.

Therefore, P-Q is divisible by 3.