For this answer I'll be using your first example: x/9 = 8/12
In the simplest terms, what the equation is saying is that x/9 is equal to 8/12. I'm assuming that the question is asking to find x, and I'll demonstrate the steps for that below.
With algebra, we do the inverse functions (i.e. multiply becomes divide, addition becomes subtraction, etc.) to find the unknown value, following inverse BEDMAS/BODMAS/BIDMAS/PEDMAS etc. etc. etc., and doing to one side what we do to the other From this, we can state that:
x/9 = 8/12
therefore
9(x/9) = 9*(8/12)
therefore
x = 9*(2/3)
therefore
x = 6