建設 と 工事 はどう違いますか？説明が難しい場合は、例文を教えて下さい。

建設する means “to build up new architectures” whereas 工事する means “to work on constructions or mechanical stuff”. 建設 suggests that the outcome is brand-new and made from scratch. In most of the cases, 工事 means repairing or enhancement.

アメリカとメキシコの間に壁を建設する。
アメリカとメキシコの間にある壁を工事する。

The former sentence means “Someone builds a new wall between US and Mexico.” The latter sentence means “Someone repairs the existing wall between US and Mexico.” Saying “...の間に壁を工事する” (i.e. omitting ある) is grammatically incorrect and very unnatural because 工事 is done with existing (damaged) objects.

On top of that, some objects of 建設 and 工事 are different. For example, you want to upgrade the air conditioner. A handyman needs to drill a bigger hole to install. In this “enhancement” case, we don’t say 建設 but 工事. 工事 can be also used for water supply, electric and gas supply etc for maintenance.