When we transform a sentence from active to passive voice, the subject of the sentence becomes the person of thing that receives an action.
In your sentence, the people who receive the action of "take good care of" are the patients. Next, the verb (i.e take) has to be transformed to "were taken".
Putting everything together, we write:
The patients were taken very good care of by the nurses.
Do note that in many passive sentences, "by" is needed to introduce the person or thing performing an action.
Hope this helps.