In an arithmetic sequence, the sum of the first $n$ terms $S_n$ is given by the formula:

$S_n = \frac{n}{2} \left( 2a + (n - 1) d \right)$

Where:

• $S_n$ is the sum of the first $n$ terms,
• $a$ is the first term,
• $d$ is the common difference,
• $n$ is the number of terms.

We are given:

• $S_9 = 216$,
• $a = 4$,
• $n = 9$.

Substitute the values into the formula:

$216 = \frac{9}{2} \left( 2(4) + (9 - 1) d \right)$

Now, simplify and solve for $d$:

$216 = \frac{9}{2} \left( 8 + 8d \right)$ $216 = \frac{9}{2} \times (8 + 8d)$ $216 = \frac{9}{2} \times 8(1 + d)$