"Why is he holding the chest?"
Translation:למה הוא מחזיק את החזה?
English here is not equivalent to the Hebrew. It would need to be: "Why is he holding his chest?" If you say "the chest" it sounds like he is holding a large wooden box, like a "treasure chest."
Nobody said (in either Hebrew or English) that it was his own chest that he was holding. Also, the sentence makes no sense in either language. You would clutch your chest or "תופס את החזה" if you were having a heart attack
In Hebrew the possessive pronoun is often left out. ie.
He is washing his hands. הוא רוחץ את הידיים
She is brushing her teeth. היא מצחצחת שיניים
In these sentences it is simply assumed that he is washing his own hands, and that she is brushing her own teeth. Sometime the את and ה are included (1st example) but they are often left out as well (2nd example).