Which of the following comets appears after every 76 years?

The correct answer is Halley's Comet.

Halley's Comet (officially designated 1P/Halley) is a short-period comet that becomes visible from Earth roughly once every 75-76 years. Its average orbital period is about 76 years, which is why it can be seen by a person, at most, once or twice in a lifetime.

It was last seen in 1986 and is next expected to return in mid-2061. The comet is named after the English astronomer Edmond Halley, who, using Newton's laws of motion, correctly predicted its 1758 return.

Among the other choices: Comet Holmes (17P/Holmes) has a period of only about 6.9 years; Donati's Comet (1858) is a long-period comet with a period of roughly 1,700-2,000 years; and Alpha Centauri is not a comet at all but the nearest star system to the Sun.