Approximately three fourths of eukaryotic proteins are composed of multiple independently folded domains. However, much of our understanding is based on single-domain proteins or isolated domains whose studies directly lead to well-known energy-landscape theory in which proteins fold by navigating through a funneled energy landscape toward native structure ensembles. The degrees of freedom for proteins with multiple domains are many orders of magnitude larger than that for single-domain proteins. Now, the question arises: How do the multi-domain proteins solve the "protein folding problem"? Here, we specifically address this issue by exploring the structure-folding relationship of Sulfolobus solfataricus DNA polymerase IV (DPO4), a prototype Y-family DNA polymerase which contains a polymerase core consisting of a palm (P domain), a finger (F domain) and a thumb domain (T domain) in addition to a little finger domain (LF domain). The theoretical results are in good agreements with the experimental data and lead to several theoretical predictions. Finally, we propose that for rapid folding into well-defined conformations which carry out the biological functions, four-domain DPO4 employs a divide-and-conquer strategy, that is, combining multiple individual folding funnels into a single funnel (domains fold independently and then coalesce). In this way, the degrees of freedom for multi-domain proteins are polynomial rather than exponential, and the conformational search process can be reduced effectively from a large time scale to a smaller time scale.