Let \( D \) be the total distance of Miguel's trip. He has driven \( \frac{2}{3} \) of the total distance in 4 hours.
This means that in 4 hours, he has covered:
\[ \frac{2}{3}D \]
We can find his speed by dividing the distance he has traveled by the time taken:
\[ \text{Speed} = \frac{\frac{2}{3}D}{4 \text{ hours}} = \frac{2D}{12} = \frac{D}{6} \text{ (distance per hour)} \]
Now, we want to determine the total time \( T \) it will take him to travel the entire distance \( D \). Since we know his speed, we can express the total time in terms of the total distance and the speed:
\[ T = \frac{D}{\text{Speed}} = \frac{D}{\frac{D}{6}} = 6 \text{ hours} \]
Thus, the total time it will take him to reach his destination is 6 hours.