There are two inequalities and we have to focus on each one individually before combining it all. Let's start with the first inequality, 0 < 4+2x, and then figure out the next one, 4+2x < 22.
So when you solve inequalities, you just do it as if the inequality sigh was an equal sign. The only exception to this is you flip the inequality sign (like from < to > or vice versa) when you multiply each side by a negative number. Fortunately, in this situation, we don't have any of that. So let's get started.
First inequality:
0 < 4+2x
-4 < 2x
-2 < x
Second inequality:
4+2x < 22
2x < 18
x < 9
From this, we can see that x < 9 but also x > -2. Therefore, we write the expression as -2 < x < 9. That means that only x-values in between but not equal to -2 and 9 can satisfy 0 < 4+2x < 22. Just plug in x-values in between but not equal to -2 and 9 into 4+2x and you'll see that they will be in between 0 and 22, meaning that the inequality is satisfied.