I’m not sure if this is exactly what the author meant, but I have the same ethos in my business.
You “over promise” in a sense that you know when you push yourself and your team, this level of “promise” can be achieved.
E.g. “Our team can make sure to increase your social media by 40% in 30 days.” — This is over-promising. But, personally for me, this over promise came from an experience and it came from formulating the strategies in my head before I give out this promise. I know that to accomplish this, we need 6 people to join the project, etc.
“Over Deliver” is the most common to all of us. When we “over promised” 40%, I might add in 1 more person just to make sure we add top value to our clients. I might cost us a bit, but the fact that we over delivered would make our clients happy and at the end of the day, that’s what matters.
Again, not sure if this is James Altucher’s take on this, but I hope this helped. :)