Approximately how many hours of daylight was there in la on june 21 of 2010?

This date, June 21st, usually marks the summer solstice, which is the day of the year with the most hours of daylight in the Northern Hemisphere and the fewest hours of daylight in the Southern Hemisphere. Now you have not specifically asked what place in the world are you interested in, so it really depends a lot on that. For example, in 2016, in the Baltic countries, depending on what city you were looking at the length of the day ranged from 17h-21h. While in the EU it ranged from 14-17h.

Hope this helps!