Lets rewrite each set of points.
(-4√2, -2√3) and (-4√2, 2√3).
Now, you can see that both points are on the same horizontal line, meaning the x values are the same. this means that you only need to consider the y values. So, to take the distance we can do 2√3 - (- 2√3). This is the same as 2√3 + 2√3, which is 4√3.