This is what SUMPRODUCT is for.

On Sheet2, A1, the formula would be:
=SUMPRODUCT((( Sheet1!$E$1:$E$10) = "Legend Lime") * ((
Sheet1!$F$1:$F$10) = "GT"))

Of course, it's much more convenient for the "Legend Lime" and "GT" to
be cell references, so the formula can be copied down a number of rows,
etc. But I think you get the idea.

Chris