How do you show a typical 6-4-3 Double Play in the scorebook? Which player's box do you show it in? I have always struggled with where to put it.

I write "6-4-3" for the batter.

For the runner, I draw a short line from 1st, half-way to 2nd, and put a small "o" at the end -- and then write "6-4" somewhere near the "o".
Others may show it differently.

(It helps if you have a scorebook like Glover's that leaves you room to write that stuff.)

Similar method here but I bring a small line across the basepath to indicate the runner was not able to advance. It's just a preference but I can see a perpendicular line better than a line with an "o" at the end. 6-4 is indicated in the advancing runners score box along with a 1 circled (assuming it is the 1st out) the I put 6-4-3DP in the batters score box with a 2 circled to indicate the 2nd out (assuming again that the first out was made at second base).