Less Than Greater Than

I have an SQL statement that I finally have working after much help from this web site. But I want to enhance it to be able to search between two dates, I have on my search form txtStartDate and txtFinish Date. I want it to read > or = to txtStartdate or txt< or = to txtFinishDate. This is my code at present. Can anyone help please?

Private Sub cmdSearch_Click()
Dim strSearch As String

If IsNull(Me.txtExerciseName) Then 'this is to ensure user keys/select at least 1 criteria; add on rest of the controlnames as desired
MsgBox "Please enter at least one criteria"

Else
quot = """"

If Not IsNull(Me.txtExerciseName) Then
strSearch = strSearch & "SELECT tblTechnicalIncidentReport.Exercise_Name,BoxNo,Fau lt, Catagory,Time_Reported,Date,Brief_Description,TopT en,TFRNos FROM tblTechnicalIncidentReport " & _
"WHERE Exercise_Name LIKE " & quot & Me.txtExerciseName.Value & "*" & quot & _
"AND BoxNo LIKE " & quot & Me.txtBoxNo.Value & "*" & quot & _
"AND Fault LIKE " & quot & Me.TxtFault.Value & "*" & quot & _
"AND Catagory LIKE " & quot & Me.txtCatagory.Value & "*" & quot & _
"AND Time_Reported LIKE " & quot & Me.txtTime.Value & "*" & quot & ";"
End If

Me.Results.Form.RecordSource = strSearch ' Update the record source, this line is to be placed at the end of all your criteria's if end if codes

' Requery the subform
Me.Results.Requery
End If

End Sub