Hello dear
You can use select_IndexChangeEvent Like this...
Protected Sub MyDropDownList_SelectedIndexChanged(ByVal sender As Object, ByVal e As System.EventArgs) Handles MyDropDownList.SelectedIndexChanged
Mytextbox.text = MyDropDownList.selectedItem.text
End Sub
And make sure Your Dropdownlist must have Autopostback property = true
Mark as solved if it helps you!!!