Answer
$(-2,5]$
Work Step by Step
The idea is to isolate x on one side.
Adding, subtracting or multiplying/dividing with a positive number preserves order (the inequality symbol remains the same).
Multiplying/dividing with a negative number inverts the order (the inequality symbol changes).
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$-6 \lt x-4\leq 1 \qquad $ ... add $4$ to all
$-6+4 \lt x-4+4\leq 1 +4$
$-2 \lt x\leq 5$
... left border excluded, right border included.
The solution set is $(-2,5].$
