The problem is how we should deal with this money.
Literal
Problem [topic-は] we [subj-が] this money [obj-を] how deal-with-should [Q-か] [copula-だ].
処理する ('process, handle, deal with') is a formal Sino-Japanese verb. すべき is the prenominal form of ~べし ('should'), creating 'how one should deal with.' The embedded wh-question serves as the predicate.