hmm.. Is there some specific reason you don't want to do it this way? Sorry but it seems a little suspicious to me.. :?
Anyway, if you do not want to to it this way, then you are asking for "privilege escalation", which is by no means something that can be given instructions for. Literally speaking, the password itself is hardly recoverable anyway since it is strongly encrypted, it can only be recovered through brute force which doesn't even worth the time to try -besides you'd need a copy of it's hash, available only to root. If it is indeed your own system, your best option is to change it, otherwise if it's not you'll not get any help
Just go at the edit prompt by selecting your kernel from the list, then press "e", then in the new list select the line that begins with "kernel ..." , go to the end of that line and enter "single" or "1" (without the quoation marks). Then press "b".
It may or may not work, depending on the runlevel 1 script configuration of Redhat.
PS. I erased your post at the other thread, since it was exactly the same and I answered here. No need to post twice