First, write down the number of days in each of our calendar months, and keep a running total. You don't have to go past August, because the Mayan calendar only had 260 days (20 x 13) as you found by examining the calendar book:
Examination of the plaque, combined with your newly found knowledge of the Mayan number system, tells you that the symbols on Witt's puzzle box are:
|8 Sep||20 May||17 Apr||12 Jul|
The equivalents in our calendar (shown in the above table underneath the Mayan dates) are calculated as follows, using the AHAU 4 to 8 Sep conversion as an example:
Now all you have to do is click on the dials until each pairing is produced, and then click on SET DIALS. You'll see the red light under the symbol change to green if you did this correctly, and the red light advances to the next symbol. The puzzle completes when you match 12 July to 11 MEN.