—How about your travel?—You can hardly imagine what difficulty we have had the vast deser

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(答案→)A. exploring
B. explored
C. to explore
D. explore
解析：考查词组：句意：--你的旅行怎样？--你很难想象我们探索广阔的沙漠是多么的不易。
实际上we have had      the vast desert.是修饰the difficulty的定语从句，词组 Have difficulty (in) doing sth，在...方面有困难，in可以省略，故选A.