lol, it is pretty bizarre I know. I just know 9 breaks into 3+3+3 because it's a square number, and adding one of those 3s to 7 makes it 10, which is easier to add stuff to, then I just get rid of the remaining 3s by adding them to 6, then 10+6 is a very easy equation to intuitively add, because you just replace the "0" with "6" to get "16" and you're done.

That's pretty much exactly how you first learn to do arithmetic. Break the (whole) numbers down into their smallest (whole) part and count em up. That's what number lines do, or using colored blocks to visually do the addition, or any number of other techniques you use when you're first learning arithmetic. I mean, even just knowing 3 + 3 = 6 is memorization, a shortcut form of 1 + 1 + 1 + 1 + 1 + 1 = 6.