Let $N_6$ be the answer to problem 6.

Given positive integers $n$ and $a$, the $n$th tetration of $a$ is defined as:
\[ ^{n}a=\underbrace{a^{a^{\cdot^{\cdot^{\cdot^a}}}}}_{n \text{ times}}. \]

For example, $^{4}2=2^{2^{2^2}}=2^{2^4}=2^{16}=65536$.

Compute the units digit of $^{2024}N_6$.

Let's think step by step and output the final answer within \boxed{}.
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