If a flight departs London (LHR/LGW) for Las Vegas (LAS) at 15:59 (3:59 PM) local time, here's the arrival calculation.
Departure: 15:59 London (GMT)
Flight time: 10h 30m
Arrival London time: 02:29+1 (next day)
Time zone diff: -8 hours
Arrival Las Vegas time: 18:29 (6:29 PM) previous day
Departure: 15:59 London (BST = GMT+1)
Flight time: 10h 30m
Arrival London time: 02:29+1
Time zone diff: -7 hours (PDT)
Arrival Las Vegas time: 19:29 (7:29 PM) previous day
The original answer ("08:59 following day") appears incorrect. A 15:59 departure from London arrives in Las Vegas the same calendar day (previous day) in the evening, due to the 8-hour time difference and ~10.5h flight.
Always verify with airline for specific date – schedules change seasonally.