To determine the total time it will take Miguel to reach his destination, we can set up a proportion based on the distance he has covered.
Miguel has driven \( \frac{2}{3} \) of the total distance in 4 hours. We can let \( D \) represent the total distance. According to the information given:
\[ \frac{2}{3}D \text{ (distance traveled in 4 hours)} \]
To find the total time \( T \) it takes to cover the entire distance \( D \), we can use the fact that the time taken to cover \( D \) will be proportional to the time taken to cover \( \frac{2}{3}D \).
Using the relationship:
\[ \frac{2}{3}D \text{ takes } 4 \text{ hours} \]
To find the total time \( T \), we can set up the equation using the ratio of the distances:
\[ \frac{2}{3}D \Rightarrow 4 \text{ hours} \] \[ D \Rightarrow T \text{ hours} \]
This implies:
\[ \frac{T}{4} = \frac{3}{2} \]
Cross-multiplying gives us:
\[ 2T = 12 \implies T = 6 \text{ hours} \]
Therefore, the total time it will take him to reach his destination is \( 6 \) hours.
The correct option is:
6 hrs