Find 4's last digit

$4^2 = 16$

$4^3 = 64$

$4^4 = 256$

$4^5 = 1024$

$4^6 = 4096$

$\vdots$

From the observation above, we get that if the exponent of 4 is even, the last will be 6.

Hence the last digit must be $\boxed{6}$

According to the cyclicity of four if the exponent is even then 6 will come as unit digit otherwise 4 will come as unit digit . $\LARGE \color{#20A900}{4}^{\color{#3D99F6}{4}^{\color{#D61F06}{4}^{\color{#624F41}{4}^{\color{#BA33D6}{4}}}}}$ Exponent will be even so 6 will come in unit's digit.

\begin{array}{c}\text{4^2=16\\4^3=64\\4^4=256\\4^5=1024\\4^6=4096\\4^7=16384\\ \vdots\quad\vdots\quad\vdots}\end{array}

Here,we can see that, when the exponent of $4$ is even, then the last digit is $6$ . And when the exponent of $4$ is odd, then the last digit is $4$ .

$\LARGE \color{#20A900}{4}^{\color{#3D99F6}{4}^{\color{#D61F06}{4}^{\color{#624F41}{4}^{\color{#BA33D6}{4}}}}}$

Here $4$ 's exponent is a even number. So the last digit becomes $\boxed{\color{#3D99F6}6}$