Which of the following terms describes a formal understanding that includes a promise backed by consideration?

The term that describes a formal understanding including a promise backed by consideration is a contract. A contract is a legally enforceable agreement between two or more parties, where each party agrees to fulfill specific obligations. The "consideration" refers to something of value that each party agrees to give or do, which is essential for a contract to be valid. This element distinguishes a contract from a simple agreement or understanding, making it enforceable in a court of law.

While a partnership is a type of arrangement where two or more individuals share the responsibilities and profits of a business venture, it does not necessarily encapsulate the formal nature of an agreement with enforceable promises. An agreement can be a broader term that may not involve enforceability or legal obligations, nor does it necessarily have to include consideration. A procedure, on the other hand, refers to a prescribed method for conducting activities and lacks the components of promises and consideration that define contracts.