For inclusion I will replace the < and > operands with <= and >=.
Not sure why you need the ActiveX controls for the drop downs - Using data validation is probably easier.
And shapes are easier to use as buttons in my opinion.
I made modifications to the file:
Book1.xlsm
Sub InterestingTest()
FirstDate = CDate(Cells(3, "I").Value)
SencondDate = CDate(Cells(4, "I").Value)
If FirstDate = SencondDate Then MsgBox "same dates bro"
Range("H8").Select
Range(Selection, Selection.End(xlDown)).Select
Range(Selection, Selection.End(xlToRight)).Select
Selection.ClearContents
j = 8
For i = 8 To 17514
CurrentValue = Cells(i, "B").Value
If Not IsDate(CurrentValue) Then GoTo NextIteration
If (CurrentValue >= FirstDate And CurrentValue <= SencondDate) Or (CurrentValue <= FirstDate And CurrentValue >= SencondDate) Then
Cells(j, "H").Value = CDate(Cells(i, "B"))
Cells(j, "I").Value = Cells(i, "C")
Cells(j, "J").Value = Cells(i, "D")
'if you are doing more than 3 or 4 of these there are better ways to do it
'if your data set is less than 6000 lines this will be fine
j = j + 1
End If
NextIteration:
Next i
End Sub