おなかが いたいから 半分 __________ 食べます。
• を
• も
• だけ
• しか

Let's see how these particles should fit in this sentence.

も - "even" "also" - often used as emphasis.
おなかがいたいからはんぶんもたべます "eat even half because my stomach hurts."
This doesn't make sense... if it was たべません then it would work because you "won't eat even half".

しか - "only" but you only use it with a negative.
はんぶんしかたべません "only eat half".

を - used when a verb is taking action on a noun.
はんぶんをたべます "eat half". This sentence works! But because of 「おなかが いたいから」it doesn't work. "My stomach hurts so I eat half" reads disjointed.

だけ - "only" used with positive verbs.
はんぶんだけたべます - "I'll only eat half".