Learn Spanish (Latin America): El perro que ladra mucho debe de tener hambre.

In Spanish, adding de after deber changes the meaning from an obligation to a strong probability or assumption. Here, you are assuming the dog is hungry because it is barking, rather than saying the dog is required to be hungry. While you will often hear native speakers drop the de in everyday conversation, deber de is the precise way to express a deduction.

Why does the sentence use tener instead of a verb for 'to be' when saying the dog must 'be' hungry?

In Spanish, physical feelings like hunger, thirst, and cold are expressed with the verb tener (to have) plus a noun, rather than ser or estar (to be) plus an adjective. tener hambre literally means 'to have hunger'. So, debe de tener hambre translates directly as 'it must have hunger'.

Would it be correct to use the subjunctive ladre instead of the indicative ladra here?

It depends on what you mean! Using the indicative ladra tells us the speaker has a specific, real dog in mind (likely one they can hear right now). If you used the subjunctive ladre, it would change the meaning to a hypothetical statement about any unknown dog: 'Any dog that barks a lot must be hungry'.

Does the word mucho need to match the gender of the dog?