Formal:
* Responsibility: This is a very common synonym, implying a moral or legal requirement to do something.
* Liability: This suggests a legal obligation, often involving financial consequences.
* Mandate: This implies a formal order or instruction.
* Charge: This emphasizes a specific task or responsibility.
* Commitment: This refers to a promise or pledge to do something.
* Obligation: This is a synonym for "duty" that emphasizes the binding nature of the requirement.
Informal:
* Task: This is a more general term for something that needs to be done.
* Chore: This refers to a routine or mundane task.
* Responsibility: This is a common informal synonym for "duty."
* Requirement: This emphasizes that something is necessary.
The best synonym to use will depend on the specific context. For example, if you are talking about a legal requirement, "liability" would be a good choice. But if you are talking about a moral obligation, "duty" or "responsibility" would be more appropriate.