Miguel has driven \( \frac{2}{3} \) of the total distance in 4 hours. To find the total time for the entire trip, we can set up a proportion.
Let \( T \) represent the total time for the trip. The distance he has left to drive is \( \frac{1}{3} \) of the total distance.
Since he has driven \( \frac{2}{3} \) of the distance in 4 hours, we can find the time it will take to drive the remaining \( \frac{1}{3} \) of the distance:
\[ \text{Time to drive } \frac{2}{3} \text{ of the distance} = 4 \text{ hours} \]
To find the time to drive the remaining \( \frac{1}{3} \) of the distance, we can use the ratio of the distances:
If \( \frac{2}{3} \) takes 4 hours, then \( \frac{1}{3} \) would take:
\[ \text{Time for } \frac{1}{3} = 4 \text{ hours} \times \frac{1/3}{2/3} = 4 \text{ hours} \times \frac{1}{2} = 2 \text{ hours} \]
Therefore, the total time \( T \) to reach his destination is:
\[ T = 4 \text{ hours} + 2 \text{ hours} = 6 \text{ hours} \]
So the correct response is:
6 hours