Remember that an absolute value is the measure of something's distance from 0 on the number line. A key piece of that idea is that distances cannot be negative.
So, any absolute value set equal to or less than 0 or any negative number cannot have any solution.
Working out way up from the bottom...
That bottom one, is clearly an issue, since you have an absolute value set less than -2.
To decide on the others, you need to get the absolute value by itself.
On the third inequality, you need to divide by -2 to get the abs val by itself. When you do that, you'll end up with |3x-5| ≤ -3/2. That's a problem, so that won't have any solution.
On the second one, you'd start by subtracting 17 from both sides and you'd get |3x-6| > -2. That'll always be true, since an absolute value is always 0 or positive.
And you have the same thing with the first inequality too, that it's already set > a negative, so it's always true.
So, just the last two will not have solutions.