You can upgrade upto 8GB with 0MB non-removable base memory and 2 memory slots

Machine name: Sony VAIO VGN-SR240J/B
CPU options: Intel Core 2 Duo (2.26GHz) Processor
Chipset: Intel GM45 Chipset
HD Bus:
Front Side Bus options:
Memory Speed options: PC2-6400 DDR2-800 200pin SDRAM SODIMM
Special notes: This machine supports maximum memory upto 8GB (using 64-bit Operating System) or 4GB (using 32-bit Operating System).