Left-handed compound bows are designed for the dominant eye, rather than than the dominant hand. As such, the minor differences between a left- or right-handed compound bow will be in respect to visual alignment, such as the side of the bow the arrow is drawn on or any attached sights. Right-handed bows will be held by the left hand and drawn with the right, which means the arrow and sights will be on the left-hand side of the bow. The opposite is true for left-handed bows.
Look for the riser's arrow stabilizer, which help secure the arrow. If it is on the left-hand side of the bow, then it is a right-handed bow. If it is on the right-hand side of the bow, then the bow is left-handed.
Inpsect for the arrow rest, which is where the end of the arrow sits when the bow is drawn. As was the case with the stabilizers, if the arrow rest is on the left-hand side, then the bow is right-handed. If the arrow rest is on the right-hand side, then the bow is left-handed.
Look for any sights, which are frequently tiny pegs protruding from the front of the bow, used for distance alignment. They will be on the left-hand side for a right-handed bow, or the right-hand side on a left-handed bow.