Well, just filtering by what you know about the connector yields about 20 possible options on digikey.
From the results, I think it's either a Hirose or JST connector.
Looks pretty close.
Also looks about right. However, it's black.
Is also promising.
One critical thing is that there may be markings on the header for the cable, rather then the connector itself. Since you say this is an xbox of yours, I assume you have both ends for the connector.
Considering that most of these headers are about 75 cents each, it may be perfectly reasonable to just buy a few of each, and try them.
The trick here is filtering.
Start at the digikey "Rectangular Headers, male pins", and start filtering by what you know:
- 12 Pins
- "Connector Type" - "Header, Shrouded"
- "Pitch" - "0.079 (2.00mm)"
- "Number of Rows" - 2
- "Mounting Type" - "Through Hole"
- "In Stock" checked
And that gets you down to a grand total of ~20 options.
From that 20, there look to be two or three possibilities, and the rest can be ruled-out visually. The trick is to look for the indexing tab positions.