If it's not too much, I'd appreciate some clarification for putting it together. I got a pack of hinge repair plates that you recommended and have now taken a look under the broken hinge.
Firstly, you ideally want to relocate the hinges to where they originally were, which is circled in red below:
Secondly, as others have said, you have purchased the
wrong type of repair plate:
The correct type looks like this (note the lip at the front and lack of the 35mm diameter hole):
The little lip is used to locate the repair plate against the edge of the cabinet and stop it moving whilst you fix the door. Examples of where to buy these include
Toolstation,
Screwfix and
Amazon - but you aren't helped by dunderheads in places like Amazon continually using the wrong names (all 3 of the links I posted have been verified as correct). The plates you have bought are just the wrong type - they are Kitchen
Door Repair Plates, not Kitchen
Hinge Repair Plates and are NBG for this repair.
I've watched some video tutorials but I'd struggling to see where the repair plate would fit and how I would go about securing it.
Well, if you've been on YouTube, all I can say is that there a lot of people who don't understand the difference between a door repair and a hinge repair - every one of the first 10 or so I found demonstrated a door repair
not a hinge (cabinet side) repair. This is the old problem of people on YouTube not using the correct nomenclature for objects (grrr!). Fortunately this guy gets it right (hurrah!):
Note the way he fixes the hinge cruciform plates with the "hook" facing rearwards.
With all the incorrect descriptions out there and having been supplied the wrong repair plate no wonder you were mystified!