I'd like to help a $6$ year old who already has a pretty good grasp of $2$, $5$, and $10$ times tables.
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I'm guessing you are looking for a hard data research answer, but unfortunately, the studies I know of are dubious, partly because they rely heavily on learning style myths, partly because some are funded by commercial parties pushing particular systems.
However, I can give some general advice --
My personal experience with my 7/8 year old is that Math War works very well for practice. You can play with a normal deck of cards---each player plays two cards, and announces the product, with the higher number winning all the cards. In case of tie, then there is "War", which means you put two (or more) cards face down and then have aother battle on top, with the winner taking the whole pile. You can also play the game with any set of ordinary flash cards. My son is interested to go for a long time with this...
I would also add, however, that although I have heard many people say that one must master the basic math facts before learning more advanced math concepts, I think that this is nonsense. Go ahead and talk about any kind of mathematics (at the right level) with your child.