So I purchased new 2x8gb ram but I'm going through my old computer and wondering if I can also transfer over my 2x4gb ram and effectively have 24gb ram total. Is this advisable or recommended?
It depends on ram type.
If your new system uses DDR4 and your old system uses some other ram type like DDR3 or may be even DDR2,
then no - you can't use it in your new system.
They need to be of same ram type, only then you can use them together in your new computer.
If they are both the same voltage RAM, same speed, and same CAS latency then I say do it. When you start mixing and matching speeds, low voltage with non-low voltage, and different CAS then you can run into issues.
It depends on ram type.
If your new system uses DDR4 and your old system uses some other ram type like DDR3 or may be even DDR2,
then no - you can't use it in your new system.
They need to be of same ram type, only then you can use them together in your new computer.