Try this, with start date in G1 and end date in G2. An array entered formula:
=MAX(IF($A$1:$A$3="desk 1",IF($B$1:$B$3>=$G$1,IF($B$1:$B$3<=$G$2,$B$1:$B$3))))
Array Formulae are a little different from ordinary formulas in that they MUST be confirmed by pressing CTRL+SHIFT+ENTER to activate the array, not just ENTER.
You will know the array is active when you see curly braces { } appear around the outside of your formula. If you do not CTRL+SHIFT+ENTER you will (almost always) get an error message or an incorrect answer. Press F2 on that cell and try again.
Don't type the curly braces yourself - it won't work...
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