Looks like your date data is stored as a string instead of a date data type. Can you post up some of the date string values?
The current query is finding the 7th character in the myDateString string, then grabbing the next 4 characters to use as a year string value, then converting it to a datetime data type. The year function gets the year value as an integer to compare to the 2013 integer on the right of the = sign.
SELECT * FROM tbl WHERE YEAR(CAST(SUBSTRING([myDateString], 7, 4) AS DATETIME)) = 2013;
Depending on what else is stored in the string, you could just use CONVERT(datetime, myDateString,103) > 3 days ago (getdate - 3)
SELECT * FROM tbl WHERE CONVERT(datetime, [myDateString], 103) > DATEADD(day, -3, getdate())