The graph shows the journey taken by Mary from Point A to Point C. The distance between Point A and Point B is 24 km.

1. Determine the relationship between grid squares and distance

From the graph, Point B is at $(3, 3)$, which means it is $3$ units vertically from Point A $(0, 0)$.
The distance from A to B is given as $24\text{ km}$.
So, $3\text{ vertical units} = 24\text{ km}$.

2. Calculate the total distance from A to C

Point C is at $(6, 6)$, which is $6$ units vertically from Point A.
Since $3\text{ units} = 24\text{ km}$, $6\text{ units} = 24 \times 2 = 48\text{ km}$.
Therefore, the distance between Point A and Point C is $48\text{ km}$.

1. Determine the total distance for the whole journey

From part (a), the total distance from Point A to Point C is $48$ km (since AB is $24$ km and B is the midpoint).

2. Determine the total time for the whole journey

Point B is the midpoint of the journey. The time taken from B to C is $2$ h, which corresponds to half the journey ($3$ squares horizontally). Therefore, the total time for the whole journey ($6$ squares horizontally) is $2 \times 2 = 4$ h.

3. Calculate the average speed

$\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{48}{4} = 12 \text{ km/h}$