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The number of ways in which 8 different flowers can be strung to form a garland so that 4 particular flowers are never separated is



4 flowers which are always together can be considered as one SET, 
Therefore we have to arrange one SET ( 4 flowers ) and 4 other flowers into a garland. 
Which means, 5 things to be arranged in a garland. 
And the SET of flowers can arrange themselves within each other in 4! ways. 
But, Garland, looked from front or behind does not matter. Therefore the clockwise and anti clockwise observation does not make difference. 
(5-1)! * (4!)/ 2 
= 288.
Simply :- (5-1)! * 4!/2
So Total value will be 288

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