My xperia x10 is booting again and again I just installed busybox and then my phone is rebooting again and again!!

What can I do to stop it?

I don't know how to boot it into recovery. I did it once (before I installed busybox) by clicking the back button when it's starting, but it's not working now.

I tried to do it from quick boot (while my phone stays on for a minute or less) but it doesn't work.

I have xperia x10 rooted to android 2.2 with cyanogenmod 6
Try holding the "Back" key while turning the phone on.

It sounds as if the phone is in a boot loop.  Why did you need to install Busybox in the first place?  CyanogenMod (and most other custom ROMs) already has it included.  I would recommend re-flashing CM6 again.