How, on the basis of any equality, to understand that one equality is equal to another?

Question

Mathematics

Hello.
I'm trying to take a coursera in mathematics, but apparently I don't understand the most basic things.
There are such tasks:

f(6) = 9
f(x) = g(x) + 2

Question: what points on the graph can we determine on the graph for the function g?
How is it solved:

f(6) = g(6) + 2
f(6) = 9
9 = g(6) + 2
g(6)=7

I don't even understand the first step. The author equates f(6) = g(6) + 2 - why so! nowhere is this in the condition! if it were in the condition g(x) + 2 = 9 , then one could agree. But on the basis of what the author draws such conclusions - I do not understand at all. What is it and where can you read about it?
Thank you all for your help.

Answer 1

x is a variable.
f(6) = 9 - here you know that some operation f on the variable x, in this case equal to 6, gives 9
in the second line, you need to substitute the same number 6 instead of x. But you already know from the first line that f(6 ) = 9
you get 9 = g(6) + 2, from here you find g(6)
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You are not required to know how f and g behave. All you can do is check their value for a particular x

Answer 2

This happened because the author substituted 6 instead of x for the equation f(X)=g(X)+2
f(6) = 9 from the condition, and therefore that
g(6) + 2 = 9 (because f(X ) = g(x) + 2, then it turns out that g(x) + 2 form the desired nine at f(6), but instead of X it will be 6)
g(6)=9 - 2 = 7