Can anyone explain me the meaning and usage of ‘might even be able to’ grammar please?
The adverb
even is not relevant to the main construction.
Might is a modal verb, and modal verbs are always followed by an infinitive form of a main verb (e.g. should go, could have happened, will be waiting).
If I’m quick, I might finish all my work before it gets dark.
But in your example, what follows the modal is a phrasal verb —
[to] be able to – which also takes an infinitive (both to’s are infinitive markers, rather than prepositions).
I might be able to finish all my work before it gets dark.