Hello jphelps.
the last number in the equation is the diameter of the objective lens (the one at the muzzle end of the scope). Generally a bigger objective lens gathers more light - which can be a benefit when hunting coyotes as they seem to be most active in low light conditions. Once the sun is up, the bigger objective lens doesn't make much difference that I know of.
If there are two numbers in the description, it's a fixed power scope(degree of magnification is fixed at a particular level). So, a 4X32 means a 4 power magnification and 32mm objective lens
If there are three numbers in the description, it's a variable power scope meaning the degree of magnification can be adjusted. So, if it's a 3-9X40 it means the degree of magnification can be adjusted from 3 power all the way up to 9 power, and the objective lens is 40mm. Sometimes people will write 3X9X40 but really it should be written as 3-9X40 as the numbers before the X indicate the power of magnifcation and the number after the X describes the diameter of the objective lens.
In my opinion 3-9X40 should be fine for coyotes. 4-12X40 should be fine, too. There's not much difference between the two, especially since you probably will only use the highest magnification setting while at the range.
Be sure to check the accuracy of the gun using the different powers of magnification. Where it shoots at 4X magnification may not be the same as where it shoots at 12X. Better shoot it at a few different setting just to sure you can count on it in the field.
Generally speaking the wisdom of the day is that you can get a good reliable fixed power scope for about the same money as a piece of crap variable power scope. But really, a Bushnell variable power scope will probably work fine for 99% of your shots on coyotes. In my experience, the cheap scopes are hard to get zeroed in but work fine once you get them set.
Heck, I just bought a new Handi in .223 and topped it with a Bushnell 3-9X40 so obviously I think you're on a good economical but reliable package, there.
Coyote hunting is a blast! It's a huge shot of adrenaline when you see one coming to the call. It has all the challenges of deer hunting but you only have to sit still in your stand for 1/2 hour or less, not hours our more. Plus, when you start in on those calls you never know what's going to happen - often it's nothing, but usually some kind of wildlife takes interest. I've had an owl almost take my hat off, had hawks land within FIVE FEET of me and stare me down. All manner of cats and birds seem to come to the call besides just dogs. But, coyote hunting in the Midwest is definitely NOT easy! In fact, it's really tough. If at first you don't succeed - don't give up!
