Quaedam discipula omnino tacet, quia timet ne responsum peius det.

It has three layers:

• Main clause: Quaedam discipula omnino tacet
• Clause introduced by quia: quia timet
• Clause depending on timet: ne responsum peius det

So the basic structure is: A certain student is completely silent, because she fears that...

This is one of the most important special uses of ne in Latin. After verbs of fearing, ne introduces what someone is afraid may happen. So after timet, ne is often best translated as that or that...might.

So:

• timet ne det = she fears that she may give
• timet ut det = she fears that she may not give

This is the reverse of what many learners first expect.

Because it is in a fear clause after timet. Latin regularly uses the subjunctive in clauses introduced by ne or ut after verbs of fearing.

Det is the 3rd person singular present active subjunctive of dare. The present subjunctive fits well here because the feared action is still only possible or anticipated.

Because it is the direct object of det. She is afraid that she may give an answer, so responsum is the thing being given.

Responsum is a neuter singular noun here. In this sentence, it means answer or response.

Because responsum dare is a normal Latin idiom meaning to give an answer. English often prefers answer as a verb, but Latin commonly uses a noun plus dare.

So responsum peius det literally means she may give a worse answer.

Here peius is the neuter singular comparative form meaning worse. It agrees with responsum, which is also neuter singular.

This is the comparative of malus:

• masculine/feminine: peior
• neuter: peius

So responsum peius means a worse answer.

Here it is an adjective, because it goes with responsum. It describes the noun answer.

As an adverb, peius would mean more badly or worse in the sense of modifying a verb. But in this sentence it is tied to responsum, so it means a worse answer, not answer more badly.

Latin word order is flexible, so the grammar does not depend mainly on position the way English does. Still, the order can add emphasis.

A few effects here are natural:

• quaedam discipula introduces the person first
• omnino tacet puts strong focus on her total silence
• det comes at the end, which is very common in Latin and gives the sentence a neat finish

You could rearrange parts of the sentence, but the current order is natural and clear.