The six different shoes are Boats, Boots, Clogs, Monks, Mules, and Wedges.
Only two shoes are kept to the right of the Monks.
The number of shoes kept to the left of the Mules is an odd number.
We get,

Boots are kept adjacent to the Boats, which are kept at one of the ends of the row.
Clogs are Monks are not kept adjacent to each other.
Here, case 2 is invalid.
Hence, the Clogs are kept at the left end of the row.
The final arrangement is,

Here, the Wedges are kept at the third position from the left end of the row.