How many hours are in a year?

Let’s start by assuming that you mean a year of exactly 365 days, where all of those days are exactly 24 hours long:

365×24=8760365×24=8760 This is probably the answer you were looking for.

But days are not of a standard length and neither are years.

A sidereal day (Earth’s full turn on her axis) is about 23.934¯¯¯23.934¯hours; with a sidereal year (a journey round the Sun) being closer to 365.242365.242 days:

365.242×23.934¯¯¯=8741.869365.242×23.934¯=8741.869 hours approximately.