Which one of the following methods was used only once to ratify an amendment? by approval of three-fourths of the state legislatures by approval of the president by approval of supreme court by approval of conventions in three-fourths of the states

I would say the correct answer is the last option - by approval of conventions in three-fourths of the states.
This method was used only once to ratify an amendment, and it happened when the Twenty First Amendment was ratified in 1933. This amendment banned alcohol throughout America and it repealed a previous amendment of the same nature - 18th.