6 The value of \( x \) is an integer. \[ 9

To solve the inequality \( 9 < x + 4 < 12 \), we can break it down into two parts. 1. Start with the left part of the inequality: \[ 9 < x + 4 \] Subtract 4 from both sides: \[ 9 - 4 < x \] \[ 5 < x \] This means \( x > 5 \). 2. Now, consider the right part of the inequality: \[ x + 4 < 12 \] Subtract 4 from both sides: \[ x < 12 - 4 \] \[ x < 8 \] Now we combine the two results: \[ 5 < x < 8 \] Since \( x \) is an integer, the possible integer values for \( x \) are: \[ 6, 7 \] Thus, the two possible values of \( x \) are \( \boxed{6} \) and \( \boxed{7} \).