You need to know the length of the hinge (looks like either 12 inch or 16 inch ), and the 'stack ' , which is the actual height of the hinge...either 13mm or 17mm. You'd need to completely remove the sash to change the hinges ( suggest deglazing first as lighter and easier to move unglazed). First thing then would be to put the new hinge in the window frame and see if the screw holes line up, it's not major if they don't, just means you will need to drill a 2mm pilot hole through each hinge screw hole...its best to do it now before putting hinge on frame and trying to do it holding a frame in place too.
Once you have done that , look at the sash and see how the back of the sash lines up with the existing hinge closed, now line the new hinge up as close as possible, and with a pencil mark where the hinge ends ( towards front edge of sash ) . Now remove the original hinge and line up your pencil mark with the hinge end of the new hinge , and if necessary drill new holes and fit new hinge ( always put screws in the centre of the elongated screw hole on the hinge..allows a bit of adjustment if needed). Repeat for other hinge. Refit sash and check it is closing properly before putting glass back , occasionally the hinges will need a little tweaking back or forth to get correct closing ( hence using centre of elongated screw holes), this unfortunately means taking the sash back out again! I have had to do the tweak a couple of times before getting it to fit without catching etc but most times no tweak needed
Hope this helps
