。
My actions put him in a bad mood.
Literal
I [of-の] action [by-で] he [topic-は] mood [object-を] damaged.
機嫌を損じる ('to spoil someone's mood, to offend') is a slightly formal/literary idiom. 損じる is an older form of 損なう ('to damage, to spoil, to hurt'). The で here marks the cause/means of the offense — 'by my action.' More polished than 気を悪くする, which is everyday speech.