Why are you using separate event to populate text box for file name. Write the same after showdialog code in the same button event
see this
Private Sub btn_ClientSelectTemplate_0_Click(sender As System.Object, e As System.EventArgs) Handles btn_ClientSelectTemplate_0.Click
OpenFileDialog1.ShowDialog()
Me.txtClientProject_0.Text = OpenFileDialog1.FileName
End Sub
Private Sub btn_ClientSelectTemplate_1_Click(sender As System.Object, e As System.EventArgs) Handles btn_ClientSelectTemplate_1.Click
OpenFileDialog1.ShowDialog()
txtClientProject_1.Text = OpenFileDialog2.FileName
End Sub
Private Sub btn_ClientSelectTemplate_2_Click(sender As System.Object, e As System.EventArgs) Handles btn_ClientSelectTemplate_2.Click
OpenFileDialog1.ShowDialog()
txtClientProject_2.Text = OpenFileDialog3.FileName
End Sub
Private Sub btn_ClientSelectTemplate_3_Click(sender As System.Object, e As System.EventArgs) Handles btn_ClientSelectTemplate_3.Click
OpenFileDialog1.ShowDialog()
txtClientProject_3.Text = OpenFileDialog4.FileName
End Sub