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If \lim_x\to1f(x) = 4,

find \lim_x\to12f(x).

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,

find \lim_x\to2f(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\to24f(x) = 4\lim_x\to2f(x).

Now we know

12 = \lim_x\to24f(x) = 4\lim_x\to2f(x),

which means

\lim_x\to2f(x) = 3.

Make it rain.