You can go two ways:
1)
The first thing you need to do, is see if you can know at which value of the pot the circuit gives the minimum voltage (6v).
Let's assume a value (example) 1K. At 1K , the main pot regulates the circuit to 6v. Then add a 2k pot in series with the main 10k pot and set it to 1k. I chose 2k to have some slack.
Now , with the second pot at 1K, the main pot will regulate 1k->11k. Which will give you 6v->24v (assuming if the resistance is higher, it will limit the output ). If not, change the main pot to a 9K pot.
2 ) Use both 10K pots. Set the first to zero, and regulate the second one to give 6v. Then use the first one to give the the rest of the range.
Again, assuming it wont go over 24v. If it starts to go, you will need to change the pots just as in 1) .
1) has a finer scale . 2) less work.
As far as the series goes, i was thinking something like this :
usually the pots in those circuits use the first and middle to make the resistance , because first and last always gives the maximum.
So, this should work. Assuming first and second pins for the resistance and last connect to gnd.
http://www.cpemma.co.uk/reg.html
Assuming they use a similar approach to the regulator just like an LM circuit. Which may not be right :shrug: .