Method 1 -- Ruth Niles recommended - Drill with a 23/64th bit and thread the hole with a 3/8 by 16 tap or use the threads on the mandrel.
Method 2 -- Use a drill bit 5/16 or larger up to the 23/64 and tap with a 3/8 by 16 plug tap.
With Wood -- I tend to put a bit of thin CA glue on the threads and after the CA has set (be sure it is set) lightly coat the tap with PAM spray and recut the threads.
Wood cut best if you cut the threads straight rather than backing off as taught with metal -- less tearout.
Acrylics use the larger bits than 5/16 - the threads are not as high, but you do not get as much breakage of threads. CA treatment is optional -- look for thread condition and decide.