In order to get the number of checked rows at the root-table level in client-side, you can try to use following snippet code.

function button1_onclick() {    var WebGrid1 = ISGetObject("WebGrid1");    var checkedRowsLength = WebGrid1.RootTable.GetCheckedRows().length;    alert(checkedRowsLength);            
    return true;
}

Following snippet code shows how to get the number of checked rows at the child-table level in client-side.

function button1_onclick() {
    var WebGrid1 = ISGetObject("WebGrid1");
    var rootTable = WebGrid1.RootTable;
    var childTable = rootTable.ChildTables[0];
    var checkedRowsLength = childTable.GetCheckedRows().length;
    alert(checkedRowsLength);            
    return true;
}

For your specific scenario, get the number of checked rows at child-table level based on the selected parent row, can be implemented by iterating trough the child rows and examine the Checked status.

function button1_onclick() {
    var WebGrid1 = ISGetObject("WebGrid1");
    var parentSelectedRow = WebGrid1.GetSelectedObject().ToRowObject();
    var childRows = parentSelectedRow.GetChildRows();
    var checkedRowsLength = 0;
    for (var i = 0; i < childRows.length; i++) {
        if (childRows[i].Checked)
            checkedRowsLength++;
    }
    alert(checkedRowsLength);            
    return true;
}

Hope this helps.

*Edited

Reason: asking member to post in the correct thread

Hello Madhavan,

As you may have noticed, this thread discuss about WebGrid but located under ClientUI area. In the future, please kindly post in the correct topic area as your thread subject would describe.