I would definitely see what the vet says as they can do a full exam of the duck. I can only tell you what it appears to be from pictures.
The ring around the eye looks like the crusty build up from fluid being released from the eye. I would recommend flushing the eye with saline a couple times a day. I like to use a syringe, you just want to make sure you don't blast the eye with it. I would also give it a fresh luke warm bath daily to help keep the eye clean and help remove some of the build up on the eye. I would also take a washcloth and soak it in warm warm and soak the ring around the eye to help soften up the buildup. It can take some time for the build up to go away. The terramycin mentioned above can also be used to help treat it if it has become infected.
I also looked at a couple of your other posts and the feathers looks damage and dirty even for a duck just out of the water. This could be because their molting or a possible hygiene issue, which may have lead to the eye infection. I feel like it could be a hygiene issue, because I can also see unzipped feathers in the other Pekin as well. Pekins unfortunately are sometimes not the best at keeping themselves clean. Mine never dunks her head in water unless she is swimming. Pekin sometimes require extra care to help maintain their feathers, eyes and nares that other ducks don't. Some require misting to encourage preening. I occasionally need to put mine in the pool so she will clean herself. Again, it could just be them molting. Their feathers will look poor when they are molting.
I agree with
@HollowOfWisps that Pekin do need more niacin than other ducks. Purina duck feed does contain the minimum amount of niacin most ducks need. Pekins can do ok with supplementing brewers yeast, but that is not always the case. It is more common with Pekins, but it happens even with other duck breeds. It is very possible that it is a niacin deficiency. With a Pekin, it is also just as likely to bumblefoot or some other leg injury.
I hope the vet visit goes well.
