best approach to connect tblPeopleMachine and tblMachine with lookup tables.
First, that table tblPeopleMachine IS a junction table except that you don't need the PK on it that you have: PeopleMachineID. It is redundant. Instead, the two fields PeopleID and MachineID can be combined to form a Compound Prime Key (i.e. the PK is two fields).
Your business rules would define whether both a person can share a machine with another person and/or whether a person can have two machines assigned. If NEITHER is allowed (i.e. man/machine assignments are unique), then you can put a unique index on the individual ID fields on that table even though the individual fields are NOT the PK.
Then, don't bother with sub-forms. If you have a list of machines and a list of people, then on the assignment form, I would use a combo box to select a person and/or a combo box to select a machine. Sub-forms would be overkill.
BUT if you have a person-table form OR a machine-table form used for maintenance of the underlying single-entity table, you could even add the combo box on that form to identify the man/machine assignment. Many ways to handle that problem. But try to not overthink it.
The picture that I am examining appears to have the directional relations correct. In particular, one thing to avoid is that even if you have a one person/one machine rule, do not make the links to the junction table one/one because that would affect what you would be able to do with the individual entity tables. One/many relationships include one/zero cases (i.e. a person doesn't have a machine assigned yet or a couple of spare machines are unassigned yet) so the one-many relationships are correct there.
Finally, I need to comment on this statement:
i do not want to go further into details of my model. Only technical solution.
But, you see, mapping the database to match the business model includes the technical nature of the model, not just the technical solution in the database. If you are trying to correctly map your business model then you hope to "make the map the same as the territory" and that means you MUST be open to reconsidering the nature of the mapping. The alternative is that if you run your business off of a mis-modeled database, you face the danger of having the database run the business in a way other than you really wanted. In the USA, we call this "letting the tail wag the dog." It is a bad thing.