I have a BG412H Speaker Half Stack that I just purchased for my son.
It is 8 Ohms Stereo and 16 Ohms Mono, and I need 4 Ohms Mono.
I see the BG412V is 8 Ohms Stereo and 4 ohms mono, I was wondering if I
just need to rewire the speakers or if I need a BG412V switch for my
BG412H or both?

This is what I have now

This is what I need

My switch and wiring currently look like this

I hope some one can give me step by step directions on how to rewire this,

Thank you!!!
What amp are you using with it? What impedance are the outputs of the amp?
A metal band?
A Guitar with an LFR > Korg Pitchblack > Behringer EQ > Hardwire CM-2 Overdrive Boss SD-1 > Hardwire CR-7 Chorus>
Orange Tiny Terror >
LzR Engineering 212 cab

My other amp can run Crysis
Also, the image is of the back of the switch, so the red/blue is connected to the right/output jack and the black yellow is connected to the left/input jack.

really hoping to get this info as my sons bday is coming soon, thanx.
Yes you can just rewire the cab to get it up to 16 ohms. This is really easy if you don't plan on ever going stereo with it: remove the switching and wire the speakers directly to the input jack.