With a little math, it can be figured mentally!
First, each year has a year code. 2007 was zero, and it goes up once every year - except for leap years, it goes up 2 (and when the year code is 7, it is also zero). Thus, 2010 has a year code of 4.
The month code is a little trickier. The month code for June is 5 (there is a different code for every month).
The day code is really easy, it is 21.
Now we have 3 numbers, 4, 5, and 21. We add them together to get 30.
Subtract from 30 the greatest multiple of 7 that is under 30, in this case 28.
30 - 28 = 2.
The day of the week that corresponds with 2 is Monday (Sunday is 1, and Monday is 2, etc).
The answer is: Monday.
June 21 2010 was a Monday.
The day of the week was a Saturday.
21 June 1995 was a Wednesday.
June 21 1983 was a Tuesday.
June 21 1962 was a Thursday.
June 21 1989 was on a Wednesday.
June 21 1946 was a Friday.
June 21 1952 was a Saturday.
21 June 1955 was a Tuesday.
21 June 1918 was a Friday.
June 21 1973 was a Thursday.
June 21 1982 was a Monday.