Are you talking about newly hatched chicks or chickens a couple of weeks old or older?
My pop door is about a foot above the run. My full-sized chickens have absolutely no trouble getting up on that. They don’t really hop, more of just step up there. The entrance to my grow-out coop is about 3 feet off the ground. They just fly up to get in when I use it. For 6” I don’t see a need for a ramp at all. If you have Silkies hat can’t fly, then you might need a ramp for something higher, but not for 6”.
You are “going” to use field fencing but they are already getting out? I’m a bit confused.
I’ve seen a hawk take a wild pigeon that was under a tree with low branches. The hawk was so fast the pigeon did not have a chance. Roosters and sometimes hens will give warning if they see a risk but that’s certainly no guarantee. On the other hand, I have an uncovered area about 45’ x 90’ feet in electric netting that is uncovered and have all kinds of big hawks around. I even have a bald eagle that occasionally visits the immediate area. I’ve never lost a chicken to a hawk or the eagle, though an owl got one when I was late locking them up one night. It just went into the coop and got one. I know other people do have big problems with hawks. With predators you don’t get a guarantee one way or the other.
Dogs are probably your biggest risk. Foxes and maybe even bobcats or raccoons probably rank higher than hawks or other birds of prey. Still, I can’t argue about covering the run for additional protection.
How big should your run be for 12 chickens? I don’t know. You can follow the link in my signature to get my thoughts on space, those apply to runs as well as coops. I don’t know your climate, how you plan to manage them, whether you ever plan to integrate new chickens later or allow a broody hen to raise chicks with the flock. All those and other things have an influence for the coop and run both. In general the tighter I crowd them (and sometimes I do) the more behavioral problems I have to deal with, the less flexibility I have to deal with issues as they come up, and the harder I have to work.
My suggestion is that you should be able to stand up in your run. You will be going in there and you don’t need to try to do things bending over. It’s no fun banging your head on the top either if you use something hard. The chickens won’t mind four feet or even two feet but I sure would. It’s not just about the chickens, you are an important part of this too. Taking care of the chickens should not be painful or inconvenient. If you have that four feet high fencing already maybe just use the heavier fencing down low and something less expensive up higher. Bird or deer netting will keep chickens in but it won’t keep many climbing predators out.
I don’t know what the area you have to work with looks like, but I suggest making the run as large as you can stand. Look at the length of a roll of wire and try to use it. What will you do with the left-over anyway? If you cover it, and I would, try to keep it no more than 8’ wide so the top doesn’t sag so much you have to support it. You don’t hear people complaining about having too much room but plenty complain about not having enough.
Good luck!