Please include parenthesis. Is it f(x)-8/x-1 or is it (f(x)-8)/(x-1). I'm assuming the latter. Also what is the given limit?
Edit, I see the limit now. Your notation was confusing. To answer your question, you know you can multiply limits, right? So lim x-> 1 (f(x)-8)/(x-1)=10, then you can multiply by a limit that you KNOW exists.
"Make up a new limit for f(x)". No, you cannot "make up" a limit for f(x). That limit just is. But you CAN create a new function, g(x), such that lim x-> 1 g(x)=c, some constant (you create g(x), and from this you know what the constant is)
I'll go one step further. FIRST you must multiply the limit you are given by another limit you create. Then you must add another limit to it. THEN you will be done. The tricky part is coming up with those two limits (but it'll click and make sense after the first one.).
This is the only thing you should be thinking about right now. What g(x) will make this easier? It won't solve it, there is another step coming, but what will simplify it? Also, what is the associated "c", the lim x->1 g(x)?