Number and string diddling are necessary when trying to decompose a composite date.
If you were using numerically stored date strings such as 20240422 (22 Apr 2024) then you have to divide by 10000 to get 2024 into a year variable. Then subtract (10000*yearnumber) to strip it out of the composite year number from your working number. Then divide by 100 to split out the month number Then subtract (100*monthnumber) from the previous working number to isolate the day number.
BUT you could also just express the date number as a string, using CSTR(compositedate) to change 20240422 (numeric) into "20240422" (string) after which you can use the MID function to pluck the strings out as MID(composite, 1, 4) for year, MID(composite, 5,2) for month, and MID(composite 7, 2) for day. From there you can build a date string to concatenate and form a correct date string, as CDATE( "#" & daypart & "-" & monthpart & "-" & yearpart & "#" ) to give you a proper Access date value, from which you could build a format string such as you suggested, "mmm-yy" for example. The octothorpes (#) are special syntax used by Access to "quote" a date string.
I didn't write code for you because you suggested you wanted to tinker a bit on your own. But these are the two most common ways to do what you are trying to do.