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As the problem description states, a palindrome is a string that reads the same both ways. The simplest way in J to describe this is y -: |. y, which evaluates if the input matches the reversed input entirely. Since the search space is relatively small, I will check every possible number. J will have no problem giving a quick answer.

J has a primitive called table with the form x u/ y that will compute a u b for every a in x and b in y if the dyadic rank of u is 0. Every possible product of two 3-digit numbers can be computed easily by supplying * as the dyadic verb.

NB. ~. , flattens the resuting table and uniquifies it to remove unnecessary checks later
   0 _1 { products =. ~. , */~ 100 + i.900   NB. 100 * 100 and 999 * 999
10000 998001

To find the maximum palindrome, it is sufficient to filter out each palindrome by checking each number in products for the property and computing the max by >./.

   +/ (-:|.)@":"0 products   NB. count number of palindromes, note (-:|.) is a monadic hook and is the same as y -: |. y
   # products #~ (-:|.)@":"0 products   NB. a boolean list as the left arg for # acts as a filter
   >./ products #~ (-:|.)@":"0 products   NB. finally, the answer