Your LimeSurvey version: 5.2.10
LimeSurvey hosting
Theme: Vanilla
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I am looking to add a question looking like this, but offering a short free text on the very right side instead of a checkbox. See the attachment as well. How can I achieve this? I had a look on a older post , but the thread got to confusing of the years. Your help would be appreciated. I do know how to code conditional equations, relevance and stuff, but do not know how to change the design of question type. Thanks a lot for your help. 

Such a mixture of different question types (checkbox + text) is not supported by Limesurvey.
There are some solutions based on custom JavaScript at this forum.
Some plugins also offer similar features like adding a free text field to the sub-questions of an array question, see survey-consulting.com/product/array-with...t-limesurvey-plugin/ and a preview at survey-consulting.com/wp-content/uploads...Plugin-Example-1.png .
But in this case you probably need to apply some custom JavaScript.

[double post deleted]

Thank you Mazi. 

Then I have to learn to use JavaScript in LimeSurvey. For now, I am just doing tailoring. Where do I have to look in the manual to learn how to change a question type? 

Hi, there is an example.

Based on an array(text) where some text fields are replaced by checkboxes.
 

As you seem to speak German:
You find this in my Tutorial "Joffms Tutorial 1: Matrizen" (Chapter 9) in the German part of the forum.

But here a small sample survey
 

Joffm

P.S.
This sample survey is based on the screenshot.
Therefore in the code there still is the not necessary management of exclusive options.