Agreed. I much prefer the latter, as it tells me not only the value, but the intention.
newTime = currentMillis + 21600000,
I go WTF is that number and is it right,
newTime = currentMillis + SIX_HOURS_IN_MILLIS
and I not only know at a glance what you're doing, I know what the value ought to be, so if you accidentally added/left out a zero, I can actually check it where that const is declared.