Yes, you would be able to install macOS Mojave or possibly Catalina on that Ivy Bridge system. The Intel HD 4000 is not natively supported on Big Sur or newer.
I would recommend you follow either of these UniBeast guides:
Mojave -https://www.tonymacx86.com/threads/unibeast-install-macos-mojave-on-any-supported-intel-based-pc.259381/
Catalina -
https://www.tonymacx86.com/threads/...alina-on-any-supported-intel-based-pc.285366/
This is the specification page for your Gigabyte B75M-D3H motherboard -
https://www.gigabyte.com/Motherboard/GA-B75M-D3H-rev-10/sp#sp
The main things to note when looking to hack a system such as this are these:
SSD/HDD connectors:
It only has one SATA3 port, so you should make sure your macOS drive is connected to this port.
- 1 x SATA 6Gb/s connector (SATA3 0) supporting up to 1 SATA 6Gb/s device
- 5 x SATA 3Gb/s connectors (SATA2 1~5) supporting up to 5 SATA 3Gb/s devices
Built-in Audio:
It contains a Realtek ALC 887 audio codec.
For your built-in audio to work you need to use Lilu.kext and AppleALC.kext.
It has the following
USB ports:
Rear I/O plate USB ports:
- 2 x USB 3.0/2.0 ports
- 4 x USB 2.0/1.1 ports
Internal USB Headers:
- 1 x USB 3.0/2.0 header
- 2 x USB 2.0/1.1 headers
For the USB ports to work when installing macOS you need to use USBInjectAll.kext and the relevant USB port limit patches for the version of macOS you plan to install.
It has the following
Display connectors:
- 1 x D-Sub port - VGA should not be used with macOS.
- 1 x DVI-D port - Try using this port first
- 1 x HDMI port
For your Intel iGPU to work in macOS you need to use WhateverGreen.kext and Lilu.kext.
There are a lot more steps required to hack a system, which are explained in the two guides linked above.