4x 0y 3z - 2w = 2
3x 1y 2z - 1w = 4
1x - 6y - 2z 2w = 0
2x 2y 0z - 1w = 1

What are you having a problem with ?

While we are happy to HELP we will not do the work for you.

I need a 4*4 problem that can be solve in different ways, elimination and substitution, gauss jordan, gaussian, inverse and cramers rule

It is certainly possible to solve these 4 simultaneous equations using each of these techniques. So what, specifically, is your question?

By the way, it appears you may have tried to cut and paste the equations into this site from another program, and unfortunately it dropped the '+' signs. So I assume what you meant is this:

4x + 0y + 3z - 2w = 2
3x + 1y + 2z - 1w = 4
1x - 6y - 2z + 2w = 0
2x + 2y + 0z - 1w = 1

yes, that is the equation that is needed to solve with thoose techniques, I hope you can help me with this

Please, help me, give me the answer with this, using these techniques,
1.elimination and substitution
2.gauss jordan
3.gaussian elimination
4.inverse
5.cramers rule
Thank you for those who will help me

We can't do your homework for you. Please show us what you've tried, and if you get stuck we can help you out. To get started - are you familiar with how to do any (or all) of these techniques? For example, the "elimination and substitution" technique is probably what you learned to solve simultaneous equations in 9th grade algebra class.

Yeah I know to how to do it, but I have to rush find an answer for this, because, it may get by the others, I know the gaussian elimination and gauss jordan,

Then, use the gaussian elimination. I'm sure you could have done it sine the time you posted it (which is nearly 4 hours ago now)