So if I understood you properly, below you should find a solution for your question 
So first you should open the "Assign task" or "Start task process" action (depending which you use). You may see a situation like below, that the icon to customize a form is inactive:

To activate it you have to add Nintex app to the site you store your workflow. Go to site settings, then "New", and choose "Nintex Form for Office 365":

After it is added open your workflow again.
Before editing a form be aware, that your variable is set as "Multiple lines". Click on the "Variables" button on the Workflow Designer's ribbon:

then click the variable you want to be a multiline. Be sure you have the checkbox "Initiation" checked. Then click the small gear icon next to the checkbox:

On the opened form with variable settings, check the field "Multiple lines":

Now, when you drag and drop your variable onto the Nintex Form the variable is presented as a multiline field:

The same for the "Initiation form":

Regards,
Tomasz