How are December 25 and October 31 the same numerically?

DECember 25 is OCTober 31, or DECimal 25 is converted to OCTal making the answer 31.
Octal being 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31.
Decimal being 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25.
If you notice, octal skips 8 and 9 going straight to 10. This is because octal is a base 8 number system. Decimal is a base 10 number system.
So in octal, 10 would be the same thing as 8 in decimal.
By them saying December, they are probably abbreviating it dec, and it's an abbreviation for both December and Decimal.
Same with October, oct, and Octal.
Hope this helps!