"Hij woont in het oosten."
Translation:He lives in the east.
I believe the rule (in both languages) is that if you mean the general direction on the compass, you don't capitalise it, but if you indicate a specific (geographical) region, you capitalise it (e.g. in the USA "The South" covers a specific set of southeastern states). So I guess it would depend on your interpretation, although the Dutch sentence here goes for the first option. (And in Dutch "het Oosten" with a capital mostly means Asia.)