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A black & white picture from a colour source generally means that the display does not support the TV system the device is supplying. For example, if your camcorder uses PAL (e.g. bought in the UK) and the TV is SECAM based (e.g. in France) or NTSC based (e.g. in the US), the picture can only be displayed in black in white, unless the TV supports other TV systems.
As far as I can tell, the TV system cannot be changed on your Sony camcorder model for its video output. It’s worth checking your TV manual to see if there’s an option to change its video source, as some TVs I’ve used that support other TV video systems need to have the input manually set to the TV system being supplied to its video input.
The vast majority of LCD TVs have multi-system video inputs that switch automatically, i.e. they will show the picture fine in colour whether the input is PAL, NTSC or SECAM, which is likely the picture shows up in colour on this display.