How would I know which side of an entity was right clicked by the player

Entities don't have 'sides' like blocks do.

 

What you could do however, is check the yaw bearing from the player to the target (or vice-versa) yaw to the target that would have been hit.  You can also do this on the y axis to get the pitch to the target.  This can be done using Math.atan2(z,x) to find the yaw, translating x and z to a length and then doing the same for those (Math.atan2(len,y)  (might be (y, len))...

 

From the yaw and pitch you can determine what 'side' was hit.  if yaw from player to target is between 315 <-> 45, you hit the south side, if it is between 45 <-> 135, you hit the east side.  135 <-> 225 north side hit, 225 <-> 315 is west side hit.

 

That gives you a general 'side hit', although it doesn't take care of checking actual hits vs. a bounding box.  For that you would likely need to implement some simple ray-tracing through voxels using an offset from world coordinates (see Bresenham's Algorithm for a start) to see what side you actual impacted on.