When saying "La comida mexicana es buena", we need the definite article because we are talking about Mexican food in general.
Now, "Queremos comida mexicana" means that we want some Mexican food ("some" is often not translated). "Queremos la comida mexicana" would be "We want the Mexican food", i. e. the one (we have) already mentioned or that has been offered.
Hi Gina85350, after listening to this sentence at regular and slow speed with a computer generated female voice in the exercise and a computer generated male voice at the top of this discussion page, I hear it more as as an 'H' (or Spanish 'J') followed by a less pronounced 'kee' before the 'kah-nah'. I also went to spanishdict.com and typed in 'México' and 'mexicana' (converted to 'mexicano'). The SPA phonetic spelling for mexicano was 'meh-hee-kah-noh'. They provide a video clip of a woman pronouncing both words and then prounouncing each syllable with a LATAM option and a SPAIN option. For both 'México' and 'mexicano', the 'hee' sounds somewhat like 'he-kee'. The SPAIN pronunciation clip is definitely more raspy on the 'hee', like it's coming from the back of the throat.
Edit: I forgot the Spanish pronunciation of 'x' was 'eh-kees' compared to the English 'ehks'. I am not hearing the 's' sound at all in 'mexicano' or 'México'.