I don't actually count very much when I'm assessing the quantity of something. I used to do a lot of "counting-" and "estimating-" type problems as a kid for fun, so I picked up a number of shortcuts that I used mentally. They're similar to the types of shortcuts I use when doing my "human calculator" parlor tricks. I kinda just get to the number and go from there.

It's kinda like spanning the whole problemspace in your head and transformating it into the solutionspace in one large transformation. I don't do it as a function mapping two spaces as an algebraist would do ... well, maybe I do but that's not how I conceive of it.

In a way, numbers are just like parts of my body - I don't think of how my fingers move when I type. I think of the words I want to see on the screen and my fingers type the right letters at the right time.

This analogy is actually really close, because I have "typos" in my times tables. 8x7 is 56, but 7x8 is 48. I actually had to specifically memorize 7x8 separate from the rest of the times tables. It's almost like there's a hole in the grid where 7x8 should be. (But that's not how I conceive of it.)

As for the way I think (visual, auditory, kinesthete, synesthete, etc) - I have no idea. I think I'm a balanced blend of all of them, but I don't have the crossover of senses that a synesthete has. I can mimic a photographic memory, but I can play by ear, too.