welcome to the forum, jeosen. say your date is in E1, try this array formula in E2:
=LARGE(IF($C$2:$C$10=$E$1,$B$2:$B$10),ROWS(E$2:E2))

and this formula in F2:
=INDEX($A$2:$A$10,LARGE(IF($C$2:$C$10=$E$1,ROW($B$2:$B$10)),ROWS(E$2:E2))-ROW($B$2)+1)

...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 your formula. If you do not CTRL+SHIFT+ENTER you will get an error or a clearly incorrect answer. Press F2 on that cell and try again.

Data Range
A
B
C
D
E
F
1
ITEM
SOLD
DATE
4/3/2015
2
APPLES
2
1/3/2015
2
ORANGES
3
ORANGES
5
2/3/2015
1
ORANGES
4
BANANA
6
2/3/2015
5
APPLES
7
3/3/2015
6
ORANGES
1
4/3/2015
7
ORANGES
2
4/3/2015