Having trouble on solving the following tasks

Lose the excess subscript increments. How so? The task mentions that i need to make a simple lookout table based on 2D array (without using the steinhart-hart equation).

Ok, I'll repeat: you get an analog value and you search it with equality among a (small) set of predefined values. An analog value in Arduino is an integer number between 0 and 1023. If you compare it to, say, 10 values you roughly have 1% probability to "catch" it each time.

Back to your code, it's clear that you're trying to identify the type of battery based on its weight. Each battery type has a minimum and maximum weight. You want to determine in which weight range your analog value falls. For this you need to test it against the minimum and maximum value of each range. And for this you need >= and <=, not ==.

I don't understand why using a lookup table implies using (only) ==.

If you insist on using ==, you could probably make a 1024-elements lookup table and use the analogRead result as an index into it. Total waste of RAM, IMHO, but using just 1 byte per element it could be doable (you'd be using half RAM just for that...).

(edit: sorry I assumed you would search using an integer value. If you use floats, then == is definitely out of question)