Can I make this phone in to a 4g phone

Sorry Keith, but I'm afraid you're out of luck. As the networking standards have evolved to introduce new features and faster networks, the devices that use them have to replace the older network chips with newer, updated chips that support the later standards.

The issue is that the network chip in your iPhone 4 does not and cannot support a 4G network. To make matters worse, there is no upgrade path; you can't replace that chip with one that will talk 4G because there is no such thing. They don't make those chips backward compatible so you can just replace the old chip with a newer one; the board itself has to be redesigned as well.

Sure, as a very difficult electronics project it could theoretically be done, but the amount of engineering and precise electrical reworking of the logic board would in no way be economically feasible. So unless someone wanted to do this strictly as an engineering challenge it would not be worth the time and effort to do so.

Verizon is phasing out its 3G networks and hasn't allowed any iPhones older than a 5S to be activated on its network for a couple of years now. The only way you can use a 3G device is as a replacement for an existing 3G device; in other words, if you have an iPhone 4 that is still in use and it dies, they will allow you to replace it with another iPhone 4, but that's the only kind of case where they'll let you use a 3G phone. Eventually they're going to stop supporting 3G altogether and everyone with a 3G phone will find themselves without service.

I may be mistaken, but I believe there may still be 3G networks running in Mexico, but that's going to be iffy since they are likely to be GSM rather than CDMA, which is primarily a Verizon network along with a few compatible carriers. The rest of the world mostly uses GSM, so there's really not much hope for being able to use that phone for anything other than a decent iPod any longer.