Will Some Electrician Explain this to Me?

I have a 12,000 Wat generator with a four wire 6 GA cable to hook the generator from the 50-amp outlet on the generator to a 50-amp power inlet box on my service panel. The generator end of the cable has a 4-prong male connector (ground, neutral and two hots). But the end of the cable for the power inlet box has a 3-slot female connector (ground, neutral and one hot). So, the two hot lines of the cable are connected to two prongs at the generator. But both hot lines are connected to one slot at the inlet box. Why is that?

Your generator is only producing a single phase, the house has two phases.

Take pictures of both ends. Sounds like the standard 30 AMP RV Plug, shown below




That plug is for connected a 30 AMP 120 RV cord to a 50 amp RV outlet. Of of the hot wires from the 50 side is not connected


Is there a manual transfer switch or something inside the house, by the breaker box?

I get what you're thinking on the 2 phases (I think) but the house is likely single phase 220v, very few residences have 3 phase service. The cable in the OP sounds like it was made to run a RV with 30amp service.

Single phase 240v is what pretty much all houses have and likely what your gen set is producing. The post above showing the RB cord is the most likely correct answer.
You will have to purchase a cord that is 4-wire (2 hots, neutral, ground) that will work from the gen set to your panel or disconnect/transfer switch (however you are wiring it in).

What's the model# of the Generator? Perhaps you have it wrong on the 3-prong plug, and there are 2 hots and a neutral.
Technically a generator is supposed to be grounded at the generator location, and so a 'ground' line would not need to be ran back to a service-panel inlet box as those should already be grounded itself.

Can you post a picture of the panel on your generator?

wrong answer. two legs same phase

Single phase refers to the transformer primary, the transformer secondary is what gives you two 120v legs that are out of phase.

based on that pic looks like a variant of a Westinghouse 12,000 generator - WGEN12000 - https://www.electricgeneratorsdirect.com/Westinghouse-WGEN12000-Portable-Generator/p95392.html

and the cable is 50A 240V, as I suggested earlier - so it has 2 hots and a neutral, so that you can get full 12000 watts into your home, 2 legs of 120v with a common neutral.
The 4th prong, the ground, is not used at the 3-prong twistlock plug - which is why you have a grounding lug on the panel lower right side, to ground the generator right at it's location!

OK, I can see that. And my generator is grounded to an in-ground rod. But why four wires and four prongs at the generator end if only three wires are used at the service panel end?

The generator has a 4-wire socket in case you have an application that needs a ground separated from the neutral.
The manual (online) shows how to separate the neutral from bonded (to ground) to unbonded.
If loads are remote, you do not want to have both a ground wire and a neutral wire running the distance with both bonded on both ends as then half of any neutral current WILL FLOW across the ground wire too! - no bueno!

I am not an electrician so take my opinion as such. But this i my understanding as well. Let me add...
Your home only has 3 wires fed from utility company. 2 "hot" conductors to provide 120/240 volts and a neutral. House panel is grounded and transomer from utility company is grounded for safety.

The genny hook up will replace utility hook up. So genny hook up will mimic drop from utility company.

You need to get a multimeter and verify the cable wiring if you think both hot lines are connected together at the 3 prong inlet box end. That would be bad, if it is actually wired that way you would trip breakers at the generator as it is a direct short between hots.

Yeah. After looking at gen panel, I cant see any reason for any double lug. Who hooked this up?

My bad. The wiring at the inlet box is hot/hot/neutral. The ground wire from the cable is not used. It seems I paid for a 4-wire 6 GA cable when a 3-wire cable would have done the job.

I have seen 4 wire connections that were three prong, with the ground being the casing/shell of the connector. Is it possible that this is what you have at the inlet box?