$1,2,\dots,6$ - 6 possibilities for each throw and hence total $6^4$ cases. Only 6 are favorable corresponding to $\langle 1,1,1,1 \rangle, \langle 2,2,2,2 \rangle, \dots, \langle 6,6,6,6 \rangle.$ So, required probability $ = \frac{6}{6^4} = \frac{1}{216}.$