Which of these words begins with an open syllable?

An open syllable is one that ends in a vowel sound, allowing the vowel to be pronounced with its long sound. In the word "robust," the first syllable "ro" is open because it ends in the vowel "o," which is pronounced as a long vowel sound. This characteristic fulfills the definition of an open syllable.

Looking at the other words: "basket" has a closed first syllable ("bas") ending in a consonant, "sat" is a single syllable that also ends with a consonant, and "cookie" contains a closed first syllable ("cook") that does not allow the vowel 'o' to be pronounced as a long sound. Therefore, among the options provided, only "robust" begins with an open syllable.