A and B can do a piece of work in $6$ days and A alone can do it in $9$ days. The time take by B alone to do the work is _________.

Using the Least Common Multiple method, let the total work be 18 units. Since A and B together complete the work in 6 days, their combined daily capacity is 3 units. A alone completes the work in 9 days, so A's daily capacity is 2 units. Subtracting A's capacity from the combined capacity gives B's daily capacity as 1 unit, meaning B alone requires 18 days to complete the work.

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