This could just be a timing issue. You could use a simple timeout()
to perform the first before the second, making the second CSS change wait 1000ms (or 1 second) before executing.
$('.panel:nth-child(2)').delay(2000).css('background-position','0px top');
setTimeout(function() {
$('.panel:nth-child(2)').css('background-position','-410px top');
}, 4000);
Alternatively, keep the delay for the first at 2000, and change the second to 4000, giving:
$('.panel:nth-child(2)').delay(2000).css('background-position','0px top');
$('.panel:nth-child(2)').delay(4000).css('background-position','-410px top');