Hint- Here, we will be proceeding by multiplying all the routes to obtain the total number of routes in between the final source and final destination.
According to the given problem, a car driver can reach Amritsar from Delhi through four different routes and that car driver can reach Pathankot from Amritsar through three different routes which means that the car driver can reach Pathankot from Delhi in total $4 \times 3 = 12$ ways. It is also given that the car driver can reach Jammu from Pathankot through two different routes.
Hence, the total number of routes or ways in which he can reach Jammu from Delhi are $4 \times 3 \times 2 = 24$ ways.
Therefore, the car driver knows a total of 24 routes from Delhi to Jammu.
Note- In these types of problems in order to obtain the total number of routes between any two final stations, the number of routes between all the substations are multiplied with each other.