Learn French: Nous n'allons jamais louer cette maison. - We are never going to rent this house.

In the near future tense, the negative words always go around the conjugated verb. Here, that is the helping verb aller (allons). The infinitive verb (louer) stays outside and comes right after the negative chunk.

Why isn't the word pas used here?

The phrase ne... jamais means "never". It completely replaces the standard ne... pas (not). You cannot use both together, which is why there is no pas in this sentence.

Why is it n'allons instead of ne allons?

In French, the negative word ne drops its e and attaches to the next word with an apostrophe if that word starts with a vowel or a silent H. Since allons starts with a vowel, ne becomes n'.

Why do we use cette for "this"?

Cette is the feminine version of "this" or "that". You use it here because maison (house) is a feminine word. If the noun were masculine, you would use ce instead.