Definitely 3 or 9.
If you place the dog at 6 or 12, then the beaver will be crossing over the jaws. Take a look at that beaver's back foot and you'll see how long it is from the toenails to the heel.
With the dog in the 3 or 9 o'clock position, and the beaver's back foot is going to step on the trap, there's a good chance that either the beaver's heel will be on the near jaw when it's toes are on the pan,or the beaver's heel will be on the pan and the toes across the far jaw. Either case will give you an undesired effect.
If the beaver's heel is on the jaw and toes are on the pan and it fires the trap, there is a good chance that you will get a toe catch or a sprung trap as the trap jaw lifts the heel of the beaver.
If the beaver's heel is on the pan and toes are across the far jaw when the trap fires, then there is a good chance for a fired and empty trap. When the trap fires, the jaw will lift the toes,draped across it and throw the whole foot out of the trap.
If set so that the dog is in the 3 or 9 position, it doesn't matter if the heel is resting on the pivot point of the jaws with the toes on the pan, or if the heel is on the pan with the toes on the far pivot point of the jaws. Either of these situations will usually result in a catch.
For a back foot catch, trap position can make the difference between a catch and a miss. For a front foot catch, it doesn't matter.