This is an inequality that involves three expressions: -2, 4 + 3x, and 2. I want to find the values of x that make the middle expression lie between the other two. To do that, I can subtract 4 from all three parts of the inequality, which gives me $-6 < 3x < -2$. Then I can divide everything by 3, which gives me $-2 < x < -\frac{2}{3}$. Now I can see that x has to be between -2 and -2/3, but not including those endpoints. How many integers are there in that interval? Well, there is only one: x = -1. Any other integer would be either too small or too big to satisfy the inequality. So the answer is 1. 
How many integers $x$ satisfy $-2 < 4 + 3x < 2$?