Video solution:

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Written solution:

The key idea is that if driving from coordinates $(x_1, y_1)$ to $(x_2, y_2),$ then the shortest distance is $|x_2 - x_1| + |y_2 - y_1|.$ This is often called the Manhattan distance. It is also equal to the number of horizontal blocks between the locations, plus the number of vertical blocks between the locations.

The shortest distance from $F$ to $A$ is then $1 + 2 = 3.$

The shortest distance from $A$ to $B$ is $7 + 3 = 10.$

The shortest distance from $B$ to $C$ is $2 + 4 = 6.$

The shortest distance from $C$ to $F$ is $4 + 1 = 5.$

Adding up all of these numbers, we get $3 + 10 + 6 + 5 = 24,$ which is choice C.

One small possible shortcut for the solution is to notice that when going from $B$ to $C$ to $F,$ the visit to $C$ is conveniently along a shortest path from $B$ to $F$ anyway, so we can even remove the requirement to stop at $C$ from the problem.