To solve this problem, the user needs to know basic arithmetic and the concept of adding and subtracting. The goat bounds upward three feet but slips back two, so it gains one foot in altitude each minute. The user must keep track of the goat's progress until it reaches the top of the cliff, which is at an altitude of sixty feet.

Now, let's go through each option and explain why it is right or wrong:

A. 36: This option is incorrect because 36 minutes is not sufficient time for the goat to climb the sixty-foot cliff. In 36 minutes, the goat would have climbed 36 feet but slipped back 24 feet, for a net gain of only 12 feet.

B. 60: This option is incorrect because the goat does not climb sixty feet in sixty minutes. In sixty minutes, the goat would have climbed 60 feet but slipped back 40 feet, for a net gain of only 20 feet.

C. 58: This option is correct. In 58 minutes, the goat would have climbed 58 feet but slipped back 38 feet, for a net gain of 20 feet, which is enough to reach the top of the cliff.

D. 40: This option is incorrect because the goat does not climb forty feet in forty minutes. In forty minutes, the goat would have climbed 40 feet but slipped back 26.67 feet, for a net gain of only 13.33 feet.

Therefore, the Answer is: C. 58