If Miguel has driven \( \frac{2}{3} \) of the total distance in 4 hours, we can set up a proportion to find the total time it will take him to complete the drive.
Let \( T \) be the total time needed to drive the entire distance.
Since \( \frac{2}{3} \) of the distance takes 4 hours, the remaining \( \frac{1}{3} \) of the distance will take:
\[ \text{Time for } \frac{1}{3} \text{ of the distance} = \frac{4 \text{ hours}}{\frac{2}{3}} \cdot \frac{1}{3} = 4 \cdot \frac{1}{2} = 2 \text{ hours} \]
So, the total time \( T \) can be calculated as:
\[ T = \text{Time for } \frac{2}{3} + \text{Time for } \frac{1}{3} = 4 \text{ hours} + 2 \text{ hours} = 6 \text{ hours} \]
Therefore, the total time it will take him to reach his destination is 6 hours.