I can't restore my iPhone from iTunes

Hi everyone,

I have the following problem. I want to restore my iphone 6 (iOS 12.0.1) and when I connected to my Mac computer (iOS X 10.9.5) and opened iTunes and clicked restore iPhone I get the following message: "To restore your iPhone with iOS 12.1, you need to install OS X 10.11.4 (or later) and iTunes 12.8."

When I click in software update (for my computer) nothing appears that I can update. When I try to find information about updating iTunes to 12.8 it says "...you might still be able to get some updates for iTunes (up to iTunes 12.8). Open the App Store on your Mac, then click Updates at the top of the App Store window. If any iTunes updates are available, click Install." But it doesn't give any alternative IF no iTunes update are available, which is what happens to me.

Does this mean that my Mac (which I bought in 2012) is too old for the new versions of iTunes and new iOS? And this is what is annoying about Mac...

Could anyone help? Any idea how to solve this?

Thanks in advance,

Ángela