I have a late 2008 MB also and upgraded to 8GB of memory after reading about it online. It works fine. They say Mtn Lion will work with less, but in my experience everything runs better with more. Buy more, it's a cheap and easy upgrade.
Model Name: MacBook
Model Identifier: MacBook5,1
Processor Name: Intel Core 2 Duo
Processor Speed: 2.4 GHz
Number of Processors: 1
Total Number of Cores: 2
L2 Cache: 3 MB
Memory: 8 GB
Bus Speed: 1.07 GHz
Boot ROM Version: MB51.007D.B03
SMC Version (system): 1.32f8
Serial Number (system): -------------
Hardware UUID: 9E6B9CB3-0D45-504F-8414-AF69B811DB62
Sudden Motion Sensor:
State: Enabled
Memory Slots:
ECC: Disabled
BANK 0/DIMM0:
Size: 4 GB
Type: DDR3
Speed: 1333 MHz
Status: OK
Manufacturer: 0x80CE
Part Number: 0x4D34373142353237334448302D4348392020
Serial Number: ----------------
BANK 0/DIMM1:
Size: 4 GB
Type: DDR3
Speed: 1333 MHz
Status: OK
Manufacturer: 0x80CE
Part Number: 0x4D34373142353237334448302D4348392020
Serial Number: -----------------