(related to Problem: The Laborer's Puzzle)
The man said, "I am going twice as deep," not "as deep again." That is to say, he was still going twice as deep as he had gone already, so that when finished the hole would be three times its present depth. Then the answer is that at present the hole is $3$ ft. $6$ in. deep and the man $2$ ft. $4$ in. above ground. When completed the hole will be $10$ ft. $6$ in. deep, and therefore the man will then be $4$ ft. $8$ in. below the surface, or twice the distance that he is now above ground.
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