We just adopted an Anatolian/Great Pyr mix from rescue. He is a wonderful boy 2 years old who was found out on the desert. We were told he could climb fences but he made no attempt the first few days and we thought we had given him enough to do with all of our animals to watch and lots of attention. He was just recently neutered. Last night he was out feeding with us and barking at the neighbors. We praised him and told him it was okay. The next minute we heard a rattle of the horse fence and he was gone. I didn't know if he knew his way home or not but 2 hours later the other dogs started barking and he was out at the front gate. He left from the side of the property. I know he is a very smart dog but any suggestions on how to break him from this or how to cope with this? I don't want a farmer to shoot him. Thank you.

Maybe get a taller fence?

"and barking at the neighbors. We praised him and told him it was okay"

Just a thought :-) Did you mean to encourage this behaviour in him or were you trying to reassure him? If you want him to guard your property then no problem, but if you do not want him to bark at your neighbours then you are rewarding him for barking :-)