Questions about example sentences with, and the definition and usage of "Inexperience"

A: Technically, it would be 'his inexperience will militate against his promotion' (the sentence with 'hinders' is correct as you wrote it).

For something to 'hinder', means it is made difficult and may delay or obstruct. If something 'militates' it will work against and directly discourage something. They are somewhat similar, though 'militates' has a stronger meaning.

Just to note, 'militates' is not a common word at all and you might find many people in England don't know what it means.

A: Due to

A: I don't have the experience to move a machine.
I don't have the experience to move the machine.
I don't have the experience to move this machine.

or

I'm not experienced enough to move a machine
I'm not experienced enough to move the machine.
I'm not experienced enough to move this machine.

A: Good job! This is very well technically written. Though I would prefer to remove "The" before the "Forgiveness" in the second sentence since it's not really necessary :)