Only in this way, directed by the teacher, ______work out the problem the day before.
A．had theyB．they couldC．could theyD．did they
D
考查倒裝句。當(dāng)only位于句首是，主句采用部分倒裝，助動詞提前。句意：只有按照老師指導(dǎo)的這種方法，前一天他們才能解決這個難題。結(jié)合語境可知本句描述的是過去的動作，故用一般過去時態(tài)。助動詞用did，選D。
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