Can someone help me create a addressing scheme using the 192.168.1.0/24 address space? On Remote 1 there are 60 hosts and 12 hosts and on Remote 2 there are 62 hosts and 28 hosts.

Are you saying that on 1 subnet (remote 1) there are 60+12 = 72 hosts and on the other subnet (remote 2) there are 62+28 = 90 hosts.

Use 192.168.1.0 /25 and 192.168.1.128 /25

If remote 1 is a router with 2 interfaces - with 60 hosts and 12 hosts - use 192.168.1.0 and 192.168.1.64 /26
If remote 2 is also a router with 2 interfaces - you'll need to move 1 host because you'll only have 61 available addresses for hosts using /26 192.168.1.128 and 192.168.1.192 /26

or if you can live without summary routes and virtually no room to add hosts on 2 subnets
remote 1 int 1 (60 hosts) - 192.168.1.0 /26 - int 2 (12 hosts) 192.168.1.64 /27
remote 2 int 1 (62 hosts) - 192.168.1.128 / 25 - int 2 (28 hosts) - 192.168.1.96 /27

I can't imagine why you'll just want to use 1 class c subnet since you have the entire block of 192.168.0.0 to use. Essentially 192.168.0.0 /16

Guess most likely this is a quiz question.

Guess most likely this is a quiz question.

Not necessarily. It could be a bigger company, or university where they have multiple building or offices and although the whole complex uses a /16 network a specific building, (or more likely floor or office department) has been told they can have the 192.16.1.0/24 range for their own use.

Although I would expect in that case whoever was setting it up would be of sufficient network knowledge to plan themselves.

Either way raj2160, that answer is basically perfect for what is needed.