Question

____ still half drunk, he made his way home. A. When B. Because C. Though D. As

Answer 1

中文意思是，半醉了，他回家了。从句子可以看出，用虽然连接比较好，虽然喝了半醉，他还是回家了。那么就是选C，though 有虽然的意思。
虽然喝了半醉，他还是回家了。
Though still half drunk, he made his way home.

Answer 2

C，回头好好看看省略结构和答案的词性。尽管（他）喝的半醉，但他回家了。

Answer 3

C. Though
这是让步关系