Hello Alarion,
Dell Precision M6300 supports maximum of 8 GB memory. Please click here for more details. But it also depends upon the Operating System installed. How much memory your Windows OS will recognize depends on which version of Windows you are running. 32-bit versions of Windows will see (and utilize) only 3GB or 3.5GB. To utilize more memory, install a 64-bit version of your OS. More information about OS memory maximums can be found here.
Please write back if you have any further questions.