about .net coding.....

You need to define 'SelectedIndexChanged' event and do your action there. You can set AutoPostback="true" for easy/direct implementation of it.
Sample:
.aspx file:

<asp:DropDownList id="dropDownList1"
            OnSelectedIndexChanged="SelectedIndex_Changed"
            AutoPostBack="true"
            runat="server"/>

.cs file:

void SelectedIndex_Changed(Object sender, EventArgs e) 
{
   dropDown2.Visible = false;
}

Detail here: MSDN: ListControl.SelectedIndexChanged Event[^]