Answer
The difference in the indicated base is \[{{5}_{\text{six}}}\].
Work Step by Step
Start by subtracting the numbers in the right-hand column:\[{{4}_{\text{six}}}-{{5}_{\text{six}}}\].
\[{{5}_{\text{six}}}\]is greater than \[{{4}_{\text{six}}}\]. So, we need to borrow from the preceding column.
Now, borrow one group of 6 because in the provided question we are working in base six.
This gives a sum of \[4+6\] or 10 in base ten.
Now, subtract 5 from 10:
\[\begin{align}
& \text{ 2} \\
& \begin{matrix}
\text{ 3}{{\text{4}}_{\text{six}}} \\
-{{25}_{\text{six}}} \\
5 \\
\end{matrix} \\
\end{align}\]
Now, perform the subtraction in the second column from the right.
That is, subtract 2 from 2:
\[\begin{align}
& \text{ 2} \\
& \begin{matrix}
\text{ 3}{{\text{4}}_{\text{six}}} \\
-{{25}_{\text{six}}} \\
{{05}_{\text{six}}} \\
\end{matrix} \\
\end{align}\]
The difference in the indicated base is \[{{5}_{\text{six}}}\].
