Responsible, answerable, accountable, amenable, liable can all mean subject to an authority which may exact redress in case of default.
Responsible, answerable, and accountable are very close, all meaning capable of being called upon to answer or to make amends to someone for something.
Although often used interchangeably they are capable of distinction based on their typical applications.
One is responsible for the performance of a task or duty, or the fulfillment of an obligation, or the execution of a trust, or the administration of an office to the person or body that imposes the task, duty, or trust or delegates the power.
Sometimes the to phrase or the for phrase is suppressed but still implied.
Sometimes when both phrases are suppressed, responsible implies manifest ability to fulfill one’s obligations especially by reason of developed powers of judgment and sense of moral obligation.
One is answerable to someone for something who, because of a moral or legal obligation or because of the acceptance of such an obligation for another, may be called upon to pay the penalty for a violation of the law or a neglect of duty; the term usually indicates or implies the existence of a judge or tribunal.
One is accountable to someone for something who because of something entrusted to him is bound to be called upon to render an account of how that trust has been executed.
Accountable is much more positive than responsible or answerable in its suggestion of retributive justice in case of default.
Amenable and liable especially stress subjection and suggest the contingency rather than the probability or certainty of being called to account.
One is amenable, usually to something, whose acts are subject to the control or the censure of a higher authority and who, therefore, is not self-governing or absolute in power.
One is liable that by the terms of the law may be made answerable in case of default.
Liable does not, however, always imply answerability. It may imply mere contingent obligation.