Answer: 60 inches
Explanation:
Let x be the height of son in the beginning of the year.
If the height is increased 110% at the end of the year , then his height in the end of the year = 110% of x
[since 110%=1.1]
Since, his height at the end of the year = 66 inches

Hence, the height of Mrs. Peters son in the beginning of the year is 60 inches.