Build a circuit to modify a printer's power supply
Its appeaars that the printer requires two power supplies - 32 V at up to 375 mA, and 16 V at up to 500 mA, for a maximum power consumption of 20 Watts.
The HP supply you show is only rated for 10 Watts, so would be insufficent to power the printer.  It would also be impractical to modify it to provide the two voltages the printer requires, even if it could produce the required power.