The 10-digit serial number for your AVR-3310 is either
(a) on the device carton
(b) on the rear of the device
Alternative (a)
On the device carton
The serial number is printed on a white label (picture) on the sides of the carton box.

Alternative (b)
On the rear of the device
A white label (red frame in the picture below) on the back of your A/V product contains the serial number.
