"He says that he likes those pants."

Translation: On mówi, że lubi tamte spodnie.

[TwinTip]

How exactly is że inserted here? What for?

[immery]

it is introduction of related speech: he says that=on mówi że. And while in English "that" may be sometimes unnecessary it is necessary in Polish.

[andron541997]

"podoba się" why not?

[Jellei]

If you put it in the right grammatical form, it makes sense - especially if he is in the shop wondering whether to buy those pants.

"spodnie" are plurale tantum, they don't have a singular form. Just like pants/trousers. So it's "podobają mu się" (they are pleasing to him). I think that "mu" (to him) has to come in-between 'podobają' and 'się', I don't see a better position for it.