"this" refers to the window object.
and when you are changing style property you cannot use dash(-) instead you write the properties using cammel case, so:
background-color will be
backgroundColor
Do you want to change the color of a specific element when your dropdown value is changed?
Is that specific element the "parent" of the dropdown or is another "random" element?
if what you want is change the dropdown background color, for example, your function could be:
function colorValue() {
var activeCompletedOnHold = form.active_Completed_OnHold.value;
if(activeCompletedOnHold==="Active1")
{
form.active_Completed_OnHold.style.backgroundColor="#347C17";
}
else if(activeCompletedOnHold==="Completed")
{
form.active_Completed_OnHold.style.backgroundColor='#0000FF';
}
else if(activeCompletedOnHold==="On Hold")
{
form.active_Completed_OnHold.style.backgroundColor='#FF0000';
}
}