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well - you could expand all the answers and see which is the same as the original equation - but that is the long way round.
Look at the brackets which are all 'squared'
look at teh constant term (e.g. -8 in the first example) when you square brackets you will always get the square of that value as a constant
so again in the first example you will get +64 as the constant when you expand
now - you can see that that is NOT the same as the original (the constant is +3 in the original)
So - go throught the answers and work out the resultant of the CONSTANT terms only. Only one of them works out to be +3 so that must be the answer
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However - that is a quick 'cheat' given that itis a multichoice question.
To really complete your understanding you should use the 'compete the square' method as required by the question - if you didn't have the multichoice you would have to do that...