Hors d'oeuvres fits because small dishes served before the main meal are called 'Hors d'oeuvres', which are served before dinner.

Tip fits because a waiter commonly receives a voluntary extra payment from consumers called a 'Tip'.

4 Years fits because a U.S. president serves a four-year term, so the tenure is '4 Years'.

'At' fits because the sentence needs a preposition to link the superior's judgement to the person considered most suitable.

Away fits because the phrase 'died away' means the sounds faded as the man moved toward the woods.

Promoted fits because outstanding performance leads to advancement, so the secretary was 'Promoted'.

Successful fits because it says the operation achieved its intended result despite slim chances, so the operation was 'Successful'.

Over fits because the phrasal verb 'ran him over' completes the sentence to show he was publicly run over or humiliated.

coup d'état fits because it describes a sudden, illegal seizure of power that replaces a government.

Femine fits because it names a period of severe shortage during which the land would be parched.