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Be careful not to crack the eggs.
Literal
Egg [object-を] break-not-so-as-to careful-do.
The ~ないように pattern marks negative purpose ('so as not to'), here paired with 注意する ('be careful / pay attention'). 注意する and 気をつける are near-synonyms for 'be careful'; 注意する feels a hair more formal and is common in written instructions, while 気をつける is the more everyday spoken choice.