Project Euler #4: Largest palindrome product
For increased performance I think it might make sense to enhance your loop:


Start with 999 each and count downwards, as the largest product will most likely involve bigger numbers. This allows you to implement a strategy for pruning and return earlier (see other answers and comments for details).
Count only in the range of 100-999, since 1-99 aren't 3-digit numbers.


For a cleaner code you should refactor your if clause into a separate method. Something like

private boolean isPalindrome(int product) {
    return ((product / 100000) % 10 == product % 10
         &amp;&amp; (product / 10000) % 10 == (product / 10) % 10
         &amp;&amp; (product / 1000) % 10 == (product / 100) % 10);
}


A cleaner code would for me also involve consistent formatting and use of brackets, e.g.


(product / 100000) % 10 vs product / 10000 % 10
for (int first = 1 vs for(int second = 1