Answer: The youngest possible age of June is 11 years.
Step-by-step explanation: Given that June's father is 6 times as old as June and the sum of their ages is no less than 77.
We are to find the youngest possible age of June.
Let x represents the age of June.
Then, according to the given information, the age of June's father will be 6x.
Therefore, we get
That is, the age of June is greater than or equal to 11 years.
Thus, the youngest possible age of June is 11 years.