#### Answer

(1,6]

#### Work Step by Step

$7\lt x+6\leq12\longrightarrow$ subtract 6 from each part
$7-6\lt x+6-6\leq12-6\longrightarrow$ subtract
$1\lt x\leq6$
A parenthesis indicates that 1 is not included in the solution set, while a square bracket indicates that 6 is included in the solution set.