Multiplication by a Constant Examples

If lim_{x → 1} f(x) = 4, what is lim_{x → 1} 2·f(x)?

We "pull out'' the constant to find

lim_{x → 1} 2·f(x) = 2·lim_{x → 1} f(x)
= 2(4)
= 8.

If lim_{x → 2} 4·f(x) = 12,

what is lim_{x → 2} f(x)?

We don't have enough information to figure out what the function f is, but that's not important.
We know that we're allowed to "pull out'' constants from limits, therefore

lim_{x → 2} 4·f(x) = 4·lim_{x → 2} f(x).

Now we know

12 = lim_{x → 2} 4·f(x) = 4·lim_{x → 2} f(x),

which means

lim_{x → 2} f(x) = 3.