。
I can't go because I'm busy.
Literal
Busy [because-ので] can't-go [explanatory-の].
ので gives the reason ('because busy'), softer and less direct than から. 行けない is the potential negative of 行く ('cannot go'). The sentence-final の is the soft explanatory particle — equivalent to のだ but without だ, giving it a gentler, often feminine tone. Strung together, this reads as an apologetic note declining an invitation — natural in casual speech, especially in feminine-coded register.