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My car model is Honda Fit 2004, after start the engine, I always hear a strange short noise when I swift to D gears or R gears and in a short distance, then it back to normal.

Thanks.

It would pay to have this looked at by a transmission specialist. It may not be an issue and I don't wish to be alarmist, but any strange noises from a CVT transmission (as fitted to your car) can be a cause for concern and costly if left unattended. Hopefully, a transmission service might be all that's needed, but you don't want the problem escalating. Therefore, it should be checked out as soon as possible.

Thanks, after I drive from Auckland to Christchurch, there is also a car shake.
So, should I book a AA Services or direct go to the car repair shop?

It's a little difficult to guess what the problem might be from this description, but a shake through the car could be a number of things. It could still be transmission related, but could also be wheel balance etc.
Perhaps take it to the AA Auto Service Centre for them to diagnose for you.