In order to fix the hinge by replacing the center casing, a near-complete disassembly of the system is required.
https://www.youtube.com/watch?v=dVn_m_OI... This video shows the complete process.
If you are a beginner to the repair process, I would suggest finding a local electronics repair center to do it for you. But if you are confident, then most steps for this process can be found in the touchscreen repair guide here: Nintendo 3DS XL Touchscreen Replacement
Make sure to get a good screwdriver and to be careful with the wire attachments.