If you stack the plates by the sink, I'll wash them later.
Literal
Sink [possessive-の] beside [to-に] plates [object-を] stack [conditional-ておいてくだされば], later I [subject-が] wash.
流し (kitchen sink) is a domestic vocabulary word. 積んでおいてくだされば chains 積む (to stack) + ておく (do in advance) + くだされば (if you would kindly). くださる is the honorific form of くれる — くだされば is its conditional. Polite and practical.