what type of sentences are the secret to good writing

If you're a technical writer, "a" is the answer, and it's the only acceptable answer.

If you're writing fiction, there are no secrets. A combination of all of these answers make for good fiction. For the purpose of this question, I'll assume that only one answer is allowed, and say that "c" is the answer your teacher is looking for here, but I'm also going to explain why that's actually wrong.

The teacher is probably using the word "intricate" as a deterrent because they assume readers shouldn't have "complicated or detailed" things to read in a fictional writing because readers of fiction are reading for enjoyment. If they think intricate = bad, I'd really like to hear their opinion of T.S. Eliot's "The Wasteland," or any number of Modernist/Post-Modernist writings.

Dickens and others use complex and long sentences from time to time, and no one would say Dickens was a bad writer. Long, complex sentences can be used to create a certain flow to an event, or they can be used to intentionally disrupt the reader so that they have to focus more intently on whatever is happening. 

The exact same thing can be said of short sentences. If a writer wants to give speed to an event, they'll use short sentences. "He ran. Then he ran some more. His feet floated over the tile. He slammed the door behind him. The door knob jiggled. Then a bang. His eyes darted around the room, looking for an escape. Another bang. Nowhere to go. The door frame started to give way..." That's a bad example that I made up off the top of my head, but you get the idea. 

Emotional and playful is the most obvious answer because who doesn't like emotional and playful writing? Of course, if you're dealing with the death of a loved one, or any other serious moment, "playful" isn't a very good choice.