First of all, you need to check that your connection to the device is configured correctly. So configure the computer's NIC to have a static IPv4 address in the 192.168.1.X range . . . anything other than X = 0, X = 1 or X = 255. The usual recommendation is to use 192.168.1.100
Now disconnect the power supply to the HG612. With just the Ethernet patch cable linking from the LAN2 port of the HG612 to your computer's NIC, depress and hold the reset button (with one hand) and the connect the power supply to the HG612 (with the other hand). Wait for about ten seconds, then release the reset button.
From a web-browser, enter the IPv4 address 192.168.1.1 into the browser's address bar. You should now see the Broadcom boot-loader firmware upload page. Specify the firmware image that you have, safe and ready, on your computer and start the update process. Do not be in a hurry . . . go and do something else for (say) ten minutes!
Kitz has put together a useful
page describing the process.