I can't see the picture that well but there is no C-17 that is serialed 04-4120. I am thinking that it says 4128 on the front I can definitely see the "412", but I can't see if that is a 0 or 8 for 4th digit.
For transports military usually lists the last 5 digits on the tail, so in this case it would say 44128, but the tail number is blurred but it looks like the first number is 4
I did a search on this site for C-17s that end in 4120 and found none so this is likely a 4128
04-4128/4138 Boeing C-17A Globemaster III
4129 (c/n P-129) was formerly 05-0129
4130 -- Plane marked as 44130 seen at RAF Mildenhall, UK. This may be 04-4130, which may
be 05-4130 (P-130) reserialled. This is correct
4131 named "Spirit of Thomas B. McGuire"
4138 is "Spirit of California". Delivered to 452nd AMW/AFRC Aug 9, 2005.
04-4139 was reserialed 05-5139
This aircraft would be military serial numbered: 04-4128, which is kind of the military equivelent to the "N" number
The construction number McDonnell Douglas/Boeing has for it is P-128
As for where it is based I can tell it says McGuire on the tail, which is McGuire AFB in New Jersey.