$\text{ The last digit, that is, the digit in the units place of the number }{\left(67\right)}^{25}-1\text{ is }$

$$\begin{gathered} \text{On dividing }25\text{ by }4\text{ the remainder }=1 \\ \text{Therefore, unit digit in }(67{)}^{25}=7^1=7 \\ \text{Therefore, unit digit in }(67{)}^{25}-1=7-1=6\text{ . } \end{gathered}$$