Learn Italian: L'orchidea, i cui petali sono gialli, è un fiore esotico. - The orchid, whose petals are yellow, is an exotic flower.

In Italian, the article before cui (whose) agrees with the thing being possessed, not the owner! Here, the thing being possessed is petali (petals), which is masculine plural, so we use i. Even though the orchid (the owner) is feminine, the article must match the petals.

Can I change the word order and say i petali di cui instead of i cui petali?

No, when translating "whose", cui must go directly between the definite article and the possessed noun. The exact structure is always: [article] + cui + [possessed noun]. So, i cui petali is the correct way to build this phrase.

Why does gialli end in -i?

Gialli is describing the petali (petals), not the orchid itself. Because petali is a masculine plural noun, the adjective giallo (yellow) changes its ending to -i to match.

Why does esotico end in -o if it is describing a flower from an orchid?