How do you take the limit of a composite piecewise function f(f(x))?

Question

Only the graph is given.
lim f(f(x))
x->2

I figured the way to do it was to find the lim f(x) = C then find lim f(x).
x->2 x-> C
The simple questions on Khan academy's "Limits of composite functions" on khan academy corroborate with my method in the case of two different functions. But this does not seem to work, according to the given answer.

Answer 1

have you seen this? https://www.youtube.com/watch?v=fjcHK6GGqm8