Can I hook up a Netgear extension to the maim apple router we have hooked up

Yes and no.

Yes, if the Netgear extender has an Ethernet port and you set up a permanent wired Ethernet cable connection from the Netgear extender back to the Apple router.

No, if you are asking if the Netgear extender can connect to the Apple router using only a wireless connection and extend the network that way.......since Apple designed their "extend" feature to only work with other Apple routers.

If you must use wireless to extend the network, look for a refurbished or used AirPort Express or AirPort Extreme on eBay.com. The downside to setting thing up this way is that there will be a loss of at least half of the potential speed on the network. So, the network will have greater "range", but it will be a slower network.

That still might be OK if you don't mind slower downloads from the Internet.

I understand what you are saying. Either hook it directly to the air port or get another air port correct?

Correct.