There are different answers to that question:
In an ordinary year, 240 days before it is the 18th of December of the previous year. In a leap year, 240 days before it is the 19th of December.
In an ordinary year 240 days after it is the 12th of April of the following year. If the following year is a leap year, then it is the 11th of April of the following year.
There were 138 days from March 30th 2008 to August 15th 2008.
The 15th of July 1970.
The 31st of August.
Adding 240 days to December 23, 2010 gives August 20, 2011.
The 15th of August can occur on any of the 7 days of the week, so it depends on which year you may be referring to. In 2012, when the question was asked, the last 15th of August, in 2011 was a Monday.
This number is constantly changing. If you are referring to today, August 13th, 2012, then there are 33 days until September 15th 2012.
The 21st of February 2012 is 180 days before it. The 15th of February 2013 is 180 days after it.
The total number of days between Sunday, February 5th, 2012 and Wednesday, August 15th, 2012 is 192 days. This is equal to exactly 6 months and 10 days.
15th August 1949 was on a Monday.
August 15th 1977 was a Monday.
15th August 1952 was a Friday.
15th August 1947 was a Friday.