Be Entrusted With
Undertake
noun, verbal noun
You accept and consign the job. You are going to be entrusted with this property for the winter. Don't go into room 237.
受託 is a formal word that means taking on a task someone has entrusted to you. You'll often see it in business contexts to talk about a company taking on work from another, like 業務を受託する (to undertake contract work). In legal contexts, it can also refer to being entrusted with physical items or money.
This is a jukugo word that uses the on'yomi readings of the kanji. You should be able to read this on your own.
当社はシステム開発を受託しています。
Our company undertakes system development projects.
受託案件が重なって、手が回らないんです。
I'm swamped with overlapping contract work.
我が社にとってその受託契約を受注することがどんなに重要か、分かっているよな。
You do understand how important it is for us to secure that subcontract, right?