Dear Meenakshi,
You can write the code on the Data grid view CellEndEdit and then you can retrieve the value of the text entered after this you can apply a foreach loop on the list items in the ListBox and highlight the matching item.
for e.g.
private void dgvBookedAnimal_CellEndEdit(object sender, DataGridViewCellEventArgs e)
{
String strItemName=datagridview.Rows[e.RowIndex].Cells["columnName"];
}
Hope this will help you out.
Thanks