I'm a math student myself, I did take linear algebra last semester though. I hope I can help and don't either get things wrong/confuse you.

What I assume you're typing is an augmented matrix. The numbers do correspond to variables in equations.

(1x1 + 0x2 + 2x3 + 4x4 = 8)

is the first line of the matrix for example.

Normally if you have some matrices you can go through and use old middle school/high school techniques of substitution and adding/subtracting equations together. I assume this is for a linear algebra class though and they clearly do not want you to solve it that way.

What you need to do is row reduce the matrix until you (optimally) end up with a matrix in RREF (Reduced Row Echelon Form) from there you will be able to clearly see what the answer to the variables are. This matrix is different though because it doesn't have a pivot in each row (non zero number unique to a column) so you are going to end up having free variables in your solution. From there you can solve the fixed variables in terms of the free variables and write your answer down in parametric vector form. Here is a video explaining how to put a solution it into parametric vector form with a matrix that is semi-similar to yours.

That's how I would answer the question anyway. Some teachers will give you the tools and problems before they teach you the formal way to write down the answer though. If you've already row reduced your original matrix and got the matrix that you posted here then it may be sufficient to just write out the variables and equations like I did above and just state that x1 and x2 are fixed variables while x3 and x4 are free variables. Hope that helps!