Can't calculate the exact R.H.S . Kindly help. Here's my approach. I'm also attaching the original question.

 

I'd recommend setting up a truth table or K-map for each of the three major pieces so that you can either confirm that what you end up with matches that part of the original expression, or determine that it doesn't match so that you can zoom on on where the mismatch begins.

You might start with your final answer. You claim it doesn't equal the target RHS. Are you sure?

Consider the general case of

X + X'Y

If X is True, then the entire thing is True, right? In other words, if X is True, the second term is irrelevant.

So any time that the second term has any relevance, you know that X must be False, making X' True, meaning that, when the second term is relevant, that X' will always be True and can thus be removed.

So see if you can show algebraically that

X + X'Y = X + Y

It might help to note that

X = X(1 + Y) = X + XY