adverb
1
BAD : That's really a good idea.
GOOD : That's a really good idea.
GOOD : That really is a good idea.
BAD : It was only a short trip but we had really a good time.
GOOD : It was only a short trip but we had a really good time.
GOOD : It was only a short trip but we really had a good time.
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The position of really (= very) is a matter of emphasis. Very often it comes immediately before the adjective or adverb it modifies: 'some really good news', 'a really old car'. Otherwise, it is usually placed immediately in front of the main verb: 'You really fooled me.' 'We're really enjoying ourselves.'
2
BAD : To his great amazement, little Nicola really won the race.
GOOD : To his great amazement, little Nicola actually won the race.
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Really and actually are sometimes interchangeable: 'She sold the piano for a lot more than it was actually/really worth.'
When you mean 'strange as it may seem', use actually (NOT really ): 'Instead of running away as he normally does, he actually offered to stay and help.'