My experience has been that 4 foot fencing makes for easy escape for even my heavy Orpingtons. If you have neighborhood dogs they can tear through that in nothing flat.
I prefer welded wire fencing- it runs about $100 for 100 feet of it at Home Depot, and I get the 5 foot high fencing- my Buff Orpingtons will fly out of it only if they can land on the top of the gate where it has a nice thick landing spot- so I put a vertical fence extension on the gate and no problems.
I buy the U- posts with the little green hooks built into them at Home Depot as it is easy to just hook the fencing onto it. They run about $4 each and I space them about every 8-10 feet except near the ends. My fencing isn't really dogproof but it makes for enough of a deterrent to keep coyotes away during the day for us.
One option for you is to make it double tall. But keep in mind that this wouldn't be much protection from a dog wandering around. If you are trying to protect flowerbeds from hens it might work for you if they aren't very determined to get in there. For example, I have some three foot high chicken wire around my blueberries and they don't go in there because it is too tight of a spot.