No, we cannot say that subnet C exists inside subnet A.
Subnet A has a subnet mask of 255.255.240.0, which means it includes IP addresses from 150.60.160.1 to 150.60.175.254.
Subnet C, on the other hand, has a different network ID and subnet mask, and its IP addresses range from 150.160.168.1 to 150.160.171.254.
Therefore, subnet C is on a different network and does not fall within the range of IP addresses allocated to subnet A.