I'm very confused about this question, first, why did the answer have H2 on the product side? I thought H+ ions were forming on the product side, not H2 gas? It also says 'aqueous,' which means it's in water. So, wouldn't the balanced chemical equation be, K (s) + H20 (L) ----> KOH (aq) + H+ (L)? I'm confused about how they obtained the gaseous H2. 

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Hi Sorry for late reply
Aditi H is atom and do not exist as it is very reactive. H is always H₂ in reactions like O is O₂ ,Cl is Cl₂ .K is very reactive and displaces H from water as H₂ gas. You need to balance the equation also.
2K(s) + H₂O (l) ---> K₂O + H₂

yes that makes sense i made a silly error , thank you!