Identify whether a good is giffen good or not and under what condition
Since the question is asking for clarification on a given answer, I don't think this question necessarily needs to be closed. To address your concerns:

You will recall Walras' Law states $p \cdot x = w$. That is, you spend all your money buying things, given some regularity conditions. So just figure out how much was spent in year 1 and that will give you wealth for that period. For year 2, you'll note that depending on the range for $x^2_2$, it will imply the consumer having different amounts of wealth. That will give you the information you need to find where good 1 is inferior.

It might be helpful to think about what ranges of good 2 would violate WARP, and what the ranges above and below it would mean. Hope this helps.