We've all put in our two bob with different thoughts and for in different situations and opponents habits also ,but Greynotsoold nailed it for me below:

Reverse the thought for the opposition:

Re: monitoring opponents rear hand

As a southpaw, if you don't want him to throw the right hand, keep circling to your right, away from his.
Personally, I find a lot of the 'avoid his power hand' stuff to be counter-productive and distracting. In boxing, you generally look to gain the inside punching position. In a match between boxers with opposite stances, you surrender that position by constantly stepping outside his lead foot. I think many southpaws do this because they neglect to develope a strong lead hand and come to rely on their left hand.
There is a big advantage in going to an opponent's strength- in this case, his straight right or straight left hand. That is, you know what he is going to do. If I'm an orthodox fighter, and a southpaw moves into my right hand, the punch the book says I should be throwing, what will I do? Throw my straight right hand, of course.
And then you get under it and hit the body with your left uppercut, or beat him to the punch with your right hook. This is the safest way to 'monitor' that punch; get him to throw it when you want him to throw it, then deal with it, and he'll keep doing it because it is what he is 'supposed' to do. It is a lot better than fighting scared, wondering what and when he is going to try.