We have a Ribbon Cable here. Which according to Wikipedia could be color-coded to reduce the risk of reversed connections:
To make it easier to identify individual conductors in a cable; ribbon-cable manufacturers introduced rainbow ribbon cable, which uses a repeating pattern of colors borrowed from the standard resistor color code (Brown is pin 1 or pin 11 or pin 21, etc. Red is pin 2 or pin 12 or pin 22, etc.). It is sometimes known affectionately to its users as "hippie cable" due to its distinct appearance.
Your cable seems to feature just that color scheme (Brown, Red, Orange, Yellow, Green, Blue, Violet, Grey, White, Black). Unfortunately and this is the big caveat here is pin 1 of the Pi's GPIO header at the opposite corner - where it reads "Made in the UK" on the PCB not near the USB receptacles. So you need to flip the connector around by 180°, i.e. with the cables towards the Pi not outwards. Or using your picture - with the brown cable being at the bottom, not the top. In which case brown would be Pin 1, i.e. bottom right, and red would be Pin 2, i.e. bottom left.
If in doubt use a voltmeter to check!