2. $P$ Let $f(x)=x^{3}+9 x^{2}+27 x+24$. Solve the equation $f(f(f(f(x))))=0$.

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Solution. Note that $f(x)=(x+3)^{3}-3$.

Therefore, $f(f(x))=f\left((x+3)^{3}-3\right)=\left(\left[(x+3)^{3}-3\right]+3\right)^{3}-3=(x+3)^{9}-3$;

similarly, we obtain that $f(f(f(x)))=(x+3)^{27}-3$ and $f(f(f(f(x))))=(x+3)^{81}-3$.

Thus, we need to solve the equation $(x+3)^{81}-3=0$; its root is $-3+{ }^{81} \sqrt{3}$.

Criteria. According to general rules.