You have the following inequality:
3 < x + 3 < 6
When you have a double inequality, the solution for x consists in making the inequality to the form a < x < b.
Then, to solve for x the given inequality you proceed as follow:
3 < x + 3 < 6 subtract both sides by 3
3 - 3 < x + 3 - 3 < 6 - 3 simplify
0 < x < 3
Then the solution is the interval (0,3)