Given number of obsevation = 6

Mean of observation = 8

Standard deviation of observations = 4

Let six observations are: a₁ , a₂ , a₃ , a₄ , a₅ , a₆

     Mean = (a₁ + a₂ + a₃ + a₄ + a₅ + a₆ )/6

=> 8 = (a₁ + a₂ + a₃ + a₄ + a₅ + a₆ )/6

=> 8*6 = a₁ + a₂ + a₃ + a₄ + a₅ + a₆ 

=> a₁ + a₂ + a₃ + a₄ + a₅ + a₆  = 48.............1

Now each observation is multiplied by 3. So

3a₁ + 3a₂ + 3a₃ + 3a₄ + 3a₅ + 3a₆ = 48*3

3a₁ + 3a₂ + 3a₃ + 3a₄ + 3a₅ + 3a₆ = 144

Now new mean = (3a₁ + 3a₂ + 3a₃ + 3a₄ + 3a₅ + 3a₆ )/6

                      = 144/6

                      = 24

So new mean = 24 

Given standard deviation = 4

       Variance = (standard deviation)²

=> ∑{(a_i )² /n} - ∑{(a_i ) /n}²   = (4)²

=> ∑{(a_i )² /6} - (8)² = 16

=> ∑{(a_i )² /6}  - 64 = 16

=> ∑{(a_i )² /6} = 64+16

=>∑{(a_i )² /6} = 80

=> ∑(a_i )²  = 80*6

=> ∑(a_i )²  = 480

Now each observation is multiplied by 3. So

   (3a₁ )² + (3a₂ )² + (3a₃ )² + (3a₄ )² + (3a₅ )² + (3a₆ )²

= 9*(a₁ ² + a₂ ² + a₃ ² + a₄ ² + a₅ ² + a₆ ² )

= 9* ∑(a_i )² 

= 9*480

= 4320

Now new varience = {∑(a_i )² /n} - ∑{(a_i )/n}²

                           = {4320/6} - (24)²

                           = 720-576

                           = 144

So new standard deviation = √144 = 12