Answer
The difference in the indicated base is \[{{345}_{\text{seven}}}\].
Work Step by Step
Start by subtracting the numbers in the right-hand column:\[{{4}_{\text{seven}}}-{{6}_{\text{seven}}}\].
\[{{6}_{\text{seven}}}\]is greater than \[{{4}_{\text{seven}}}\]. So, we need to borrow from the preceding column.
Now, borrow one group of 7 because in the provided question we are working in base seven.
This gives a sum of \[4+7\] or 11 in base ten.
Now, subtract 6 from 11:
\[\begin{align}
& \text{ 1} \\
& \begin{matrix}
\text{ 62}{{\text{4}}_{\text{seven}}} \\
-{{246}_{\text{seven}}} \\
5 \\
\end{matrix} \\
\end{align}\]
Now, subtract the numbers in the second column from the right: \[{{1}_{\text{seven}}}-{{4}_{\text{seven}}}\].
\[{{4}_{\text{seven}}}\]is greater than \[{{1}_{\text{seven}}}\]. So, we need to borrow from the preceding column.
Now, borrow one group of 7 because in the provided question we are working in base seven.
This gives a sum of \[1+7\] or 8 in base ten.
Now, subtract 4 from 8:
\[\begin{align}
& \text{ 51} \\
& \begin{matrix}
\text{ 62}{{\text{4}}_{\text{seven}}} \\
-{{246}_{\text{seven}}} \\
45 \\
\end{matrix} \\
\end{align}\]
Now, perform the subtraction in the third column from the right.
\[\begin{align}
& \text{ 51} \\
& \begin{matrix}
\text{ 62}{{\text{4}}_{\text{seven}}} \\
-{{246}_{\text{seven}}} \\
{{345}_{\text{seven}}} \\
\end{matrix} \\
\end{align}\]
The difference in the indicated base is \[{{345}_{\text{seven}}}\].
