Can a computer have 60 GB of RAM in it?

Yes, it can.

However, most systems will prefer memory in powers of two, and are thus more likely to support 64GB than 60GB. Most current consumer computers support less memory, e.g. 32 or 16GB. The memory limit is determined by the motherboard and system BiOS; you will need to check with the specific system's documentation to determine the limit for the given system.

Note that not all operating systems are capable of handling memory of this size.