Im building a M13-40 Italian tank to go with my Ariete MBT
for a past and present theme and Im wondering what kind of painting options I have for the M13-40 as far as accurate or close to accurate colors and cross reference to AK paints any hepl will be appreciated

https://tanks-encyclopedia.com/ww2/italy/Carro_Armato_Medio_M13-40.php
Some at the bottom of the page.

Lifecolor makes a ww2 Italian Army set.
Should be able to order just the colors you need.

Hataka is another option. https://www.bing.com/images/search?view=detailV2&ccid=y7JDZwTY&id=C8DB9002E153AC9084507B33AB44BED286B85649&thid=OIP.y7JDZwTYatr450Ksty8y6wHaD6&mediaurl=http%3a%2f%2fhataka-hobby.com%2fmodelarstwo%2fuploads%2f2019%2f03%2fas106_Back.jpg&exph=919&expw=1742&q=italian+army+paint+sets&simid=608049343030495272&selectedIndex=5&qpvt=italian+army+paint+sets&ajaxhist=0

Any idea what the paints cross reference to in Tamiya or AK?

Do you have the Tamiya kit or something else? The Tamiya instructions have Tamiya paint references in them.

Looking online at the instructions, the sand color is 2 parts XF-60 to 1 part XF-59. The green camouflage color is 2 parts XF-65 to 1 part XF-58.

No idea how those colors translate to AK, though the "real colors" range of AK paints should have obviously labeled colors (saying Italian WWII or something like that).