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Answer

On multiplying the whole equation by 2 , the equation turns into 

8a^3+ 18b^2 + 2c^2 - 12ab - 6bc - 4ca =0 

now arranging these as sum of square we get, 

(2a - 3b)^2 + (3b - 3c)^2 +(c - 2a)^2 =0

since sum of all the squares is equal to zero 

so we can equate each square individually to zero.

2a - 3b = 0 => 2a = 3b. 
3b - 3c =0 => b = c 

3b =c and c = 2a 

(4a+c)/b = 9 

Answer

Given equation is multiply with 2 

Than 

(2a-3b)^2+(3b-c)^2+(c-2a)^2=0

Than (2a-3b)=0

3b-c=0

c-2a =0

a/b=3/2

c= 6

Than 4a+c/b =12+6/2=9 answer 

Answer

Ans. (B) 9

On multiplying the given equation by 2, and then arranging as the sum of 3 squares, we get

(2a - 3b)² + (3b - c)² + (c - 2a)² = 0.

Since, sum of all squares = 0, each square = 0.

So, 2a - 3b = 0  => 2a = 3b.

Similarly, 3b = c and c = 2a.

Now, (4a+c)/b = 3c/(c/3) = 9

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