8k - What he took with him, this isn't in dispute.
3k - Lets say this is the number he has for patrolling war camp and bandits, could be too high, but all guess work.
3k - My guess is 3k (which could be completely wrong) due to him not taking ALL his able body men. There was a quote somewhere where he mentions not taking as many as he normally does because he is teaming up with Sadeas. So this would be the amount of men that he would normally take that he left behind. (that isn't part of the bandit/war camp troops)
All that, if true, would put him at 14k or so at the warcamp, so I guestimated around 6k troops left at home. Which again, is just a guess and could be completely wrong, but a ot of times projection strength isn't anywhere near your full strength (have to keep the homeland secure).
Found this quote:
“We need troops, Dalinar,” Sadeas said. “Lots of them. How many men could you field, at maximum?”
“On short notice?” Dalinar said. “Eight thousand, perhaps.”
So as far as what qualifies in short notice, no idea.