Here "detestable things" refers to idols, which God hates. Alternate translation: "their disgusting idols" (See: [[rc://en/ta/man/translate/figs-metonymy]])
This is a metonym for Yahweh's temple. It can be expressed in active form. See how you translated this in [Jeremiah 7:10](./10.md). Alternate translation: "house that belongs to me" or "temple where they worship me" (See: [[rc://en/ta/man/translate/figs-metonymy]] and [[rc://en/ta/man/translate/figs-activepassive]])