Firstly, I focussed on "If you remove my 1st & 2nd letters, you can't see me". The first thing that comes to mind which we can’t see is the "AIR".
So now, what 4 letter words can be formed ending with "AIR"? Think of all the words from A to Z, considering which one lies above you. That is how we get to "HAIR".
Now, which 5 letter word can be formed ending with "HAIR"? Starting with A to Z, we reach "CHAIR" and also, it lies below us.
And the required answer is "CHAIR".