How many hours are in a year?
Generally a number that strikes in our mind for number of days in a year is obviously 365, but when it comes to “ calculate total hours in a year” you must know these different types of years which varies in very few fractions but can change the result of hours in a year.
Let’s just have a glance at the type of years and the accurate number of days to calculate hours in whole year:

Draconic(eclipse) : 346.62 days

Lunar : 354.37 days

Vague, a common year in many calendars : 365 days

Tropical(Solar) : 365.242189 days

Gregorian : 365.2425 days

Julian : 365.25 days

Sidereal : 365.25636 days

Anomalistic : 365.259636 days

Leap year : 366 days
Now let’s see the total number of hours of the main years below:

1 common year (Vague) : 365 days = (365 days) × (24 hours/day)
= 8760 hours 
1 leap year = 366 days = (366 days) / (24 hours/day)
= 8784 hours 
1 Julian year = (365.25 days) × (24 hours/day) = 8766 hours

1 Sidereal year = (365.25636 days) × (24 hours/day) = 8766.15264 hours

1 tropical year = (365.242189 days) × (24 hours/day) = 8765.812536 hours
Time is a human construct. From planck time to supereons. They are relative units of measure. Likewise, hours and years are something humans created to keep track/record, predict and categorize based on Earth’s orbit and its revolution around the Sun. There is not a static number of hours in a year, for instance, if you consider leap years, they are 24 hours longer. So approximately 8784 hours in a leap year on Earth. If we lived on Mars, we would experience 16,500 hours 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.