how to i find out how many external displays my 16" MacBook pro m3 will support?

If that is a 16” model, it has either a M3 Pro chip or a M3 Max chip. Which chip you have determines the maximum number of external displays: up to two (M3 Pro) or up to four (M3 Max).

MacBook Pro (16-inch, Nov 2023) - Tech Specs - Apple Support

Hi,

Following document could help you question.

How many displays can be connected to MacBook Pro - Apple Support

The same rules we learned for the M1 and M2 and M3 mostly still apply to the M4 models. Display interfaces are generated deep inside the system on a chip. How many there are depends on the exact type of Processor:

M3 (plain) like the 13-in and 15-in supports up to ONE External fully hardware-accelerated external display.

Except the M3 MacBook Air models with 13 or 15-in display, (and certain M3 plain MacBook Pro models when running 14.6 or later) which can support a second External display instead of the built-in display when you close the cover on the built-in display. This may require MacOS 14.6 or later.

M4 (plain) supports up to Two fully hardware-accelerated External displays (three for Mac mini)

M4 PRO processor supports up to Two fully hardware-accelerated External displays. (three for Mac mini)

M4 MAX processor supports up to Four fully hardware-accelerated External displays.

M4 ULTRA processor supports up to Eight fully hardware-accelerated External displays