6,272 in organized folders by save game.
The total number of screenshots ever taken though is at least double, probably triple that amount. I take a ton of screenshots, but only keep one of each if there are duplicates from selfies or from my Sim photographers taking shots. Whenever I start a new save game, I create a folder for it on my hard drive and after a gaming session, I remove any screenshots taken from the in-game folder and put them in their respective folders on my hard drive.
Some of these folders have sub-folders. For example my Build-N-Share folder has a folder for each round I've entered, legacies for each generation, each regeneration of my Time Lady, The Artist, for the Time Lord Challenge and folders for rounds of other contests/challenges, etc. I also create sub-folders in these save game folders for tray files of Sims/builds too.
Helps keep things organized and prevents lag from having so many screenshots in-game. At least that was the case in the past on my old laptop. I could probably get away with leaving some in-game now with my new gaming desktop. But it's become a habit that I enjoy so I keep doing it. It's fun to look back at these from time to time for older saves that I haven't played in awhile or just to reminisce on completed challenges/contests. :)
EDIT: The main folder where all these folders of screenshots, tray files, plus copies of save games and other miscellaneous stuff is 11.2 GB. lol Yeah, I've played TS4 a lot over the last 4+ years. <3