On the plus side the
MacBook4,1 has not only a 64-Bit CPU but also a 64-Bit EFI. But that's about it, because...
The problem is the integrated graphics processor (GMA), in the case of the MacBook "Core 2 Duo" Early 2008 aka
MacBook4,1 the Intel GMA X3100. There are only 32-bit drivers (in OS X terms: kexts) available. Since OS X 10.8 Mountain Lion the OS is exclusively 64-Bit.
Apple did try to get 64-Bit drivers for the Intel GMA950 as well as the GMA X3100. They were even briefly included in Mac OS X 10.6.2 Snow Leopard. They had only very basic functions (I think they lack support for both Quartz Extreme and Core Image) and were in a very early develpment state.
The problem is that without the graphics drivers the OS doesn't work.
There are unofficial attempts to get Mountain Lion (10.8), Mavericks (10.9) and Yosemite (10.10) on those otherwise unsupported Macs. One of those attempts is MacPostFactor and macOS Extractor by OS X Hackers. AFAIK only Mountain Lion (10.8) works with the incomplete 64-Bit drivers from Mac OS X 10.6.2. It seems to be possible to get up to El Capitan (10.11) but all of it without accelerated graphics. If you search the Internet you will find verious reports, e.g. this guide on MacRumors for OS X Yosemite (10.10).
In any case such an endeavor is not trivial.