welcome to the Plugin Café and thank you for reaching out to us. Please read our Forum Guidelines which explain the procedures used in this forum. Your topic is missing the version of Cinema 4D you are using among other information. The version(s) should be expressed as tags of the topic, as lined out in the forum guidelines. I am sorry for pointing this out so bluntly, but the version is important. I assume you are using R23 from the screenshot.
What you want to do is certainly possible to do and for an experienced Cinema 4D developer also not that hard to do, but the API for the take system can be a bit daunting for beginners. I must also point out that we cannot provide code unless you have provided code with a concrete question.
From your description I understand that you what to create n takes for a document that contains n layers and then set the solo mode parameter of each such layer that is being wrapped by a take. I would first point to the official take system example scripts on GitHub which will explain most aspects of the take system API. There were recently also the topics How can I get a Layer's objects with Python? and Changing material projection in takes using Python here on Plugin Café, which talked about takes + layers and takes + parameters. There are also quite a few more threads in this forum on the take system, I would encourage you to search yourself for the ones that best fit your information needs.
You must principally iterate over all layers attached to a document and then add a take for the solo parameter of each layer. You can access the layers of a document with
BaseDocument.GetLayerObjectRoot() and add takes with the c4d.modules.takesystem module. The central method in the take system module to add parameter overrides is BaseTake.FindOrAddOverrideParam. The solo mode of a layer is just a parameter as any other, it can be written with c4d.ID_LAYER_SOLO. The two threads I mentioned contain code with most of the building blocks for doing that. When you want more explicit help, you will need to provide some code of what you have done and where your problems are.