There's absolutely no way I can finish that work by tomorrow.
Literal
Tomorrow [by-までに] that work [object-を] finish [nominalizer-こと] [topic-は] absolutely cannot.
どうしてもできません — 'absolutely cannot' — uses どうしても with the negative to mean 'no matter what, it can't be done.' こと nominalizes 終える into the subject of できない. The tone is emphatic refusal/impossibility.