Mandarin is represented in characters. Each character is a single syllable. A guide can be found here showing the pronunciations as romanized in Pinyin (alternative romanization patterns exist but are rarely used today).
If a "word" is defined as a single character, then yes, all words are a single syllable. This is likely the interpretation your instructor intended. However, if a word is defined as a unique concept (whichwehappentoseparatewithspacesforconveniencebuthavehistoricallybeenruntogetherwithoutlosingtheirinherentmeaningandindividuality) then there are many words that are composed of multiple characters and therefore multiple syllables. There are only about 2000-3000 characters in use, but of course there are many many more "words" available.
The word for bus is a decent example of this. It is a four character compound word: 公共汽车.
- 公 gōng (public)
- 共 gòng (public, common)
- 汽 qì (steam or vapor)
- 车 chē (vehicle)
Each of these characters has its own meaning. There are additional combinations: A 汽车 is a car. 公共 applies to things generally publicly operated. And a 公共汽车 is a public bus. No one conceptually thinks "publicly sponsored community use steam powered vehicle."
The same is true for pretty much every compound word: a bicycle is a 自行车 (personal vehicle), accent is 口音 (mouth sound), etc.