If \lim_x\to1f(x) = 4,
We "pull out'' the constant to find
\lim_x\to12f(x)& = &2\lim_x\to1f(x)& = &2(4)& = &8.
If \lim_x\to24f(x) = 12,
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\to24f(x) = 4\lim_x\to2f(x).
Now we know
12 = \lim_x\to24f(x) = 4\lim_x\to2f(x),
\lim_x\to2f(x) = 3.
Make it rain.