propose doing sth

Hi, everyone. I find the construction of propose doing sth in the dictionary.
In my impression, the construction is wrong. But I'm not sure. I wonder what is the difference between propose to do and propose doing.

I remember:
When propose means "to suggest", "propose doing something" is used only.
When propose means "to intend", "propose to do something" is used only.


The constructions in the dictionary confuses me.
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2 [transitive] (formal) to intend to do something
propose to do something
What do you propose to do now?
propose doing something
How do you propose getting home?
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Does "How do you propose getting home?" means "how do you intend to get home?"

Thanks

It means "how do you suggest getting home". You will find that many verbs can take either an infinitive or a gerund or both.