。
I suggested he step back and wait for things to calm down.
Literal
I [topic-は] him [to-に] self [object-を] pull-[sequential-て] situation [subject-が] settle [nominalizer-の]-[object-を] wait [in-the-way-ように] recommended.
A complex multi-clause sentence. 身を引く ('step back, withdraw,' literally 'pull one's body back'). 事態 ('situation, state of affairs'). 落ち着く ('to settle down, calm down'). ~を待つ takes a nominalized clause as object. ~ように勧める ('suggest/recommend that...'). Formal-flavored advice chained together.