COUNTIFS() with an S allows the ability of multiple criteria and you can bracket the dates:
=COUNTIFS('Sheet1'!L:L,">=15",'Sheet1'!D:D, ">=" & DATE(2015,1,1),'Sheet1'!D:D, "<=" & DATE(2015,12,31))
If your dates are actually text strings that look like dates you can do the:
=COUNTIFS('Sheet1'!L:L,">=15",'Sheet1'!D:D,"*2015*")