。
She divided the cake into six pieces.
Literal
She [topic-は] that cake [object-を] into-6-pieces divided.
~に分ける ('divide into X') uses に to mark the resulting state — into how many pieces, into what categories. The 'into-state' に is the same one in ~になる, ~にする, ~に変える: a particle for end-state. ６つ uses the native Japanese counter ~つ, which works for general objects up to ten (1–10: ひとつ, ふたつ … とお) before giving way to 11以上 with kanji-based readings. ケーキ is the loanword most native English speakers will recognize; in everyday Japanese cake-eating contexts it dominates over native words like 菓子.