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Here we take the distribution function as cumulative distribution function and not probability density function..Reason bein when we integrate the probability density function over the interval , we get the probability over the interval..Now this probabiltiy should be greater than or equal to 0 or less than or equal to 1.But here when we integrate the function over interval from x = 2 to x = 4, the value comes out to be greater than 1 which is wrong..Hence we take the given distribution function as cumulative distribution function.. Cumulative distribution function of a random variable x means :

If a value of  a random variable is F(x) then it means probability the random variable takes any value <= x is given by F(x)..

So  to find  P(2  <=  x  <  4)   ,  we need to find F(4) and F(2) and then perform F(4) - F(2)..

So according to the piecewise definition of function given in the question :

F(4)    =   1 [ Here we take 3/4 and not 1 bcoz we are asked the probability of x < 1 and not x <= 1 ]

F(2)  =    3/5  =  0.6  [Here we have taken 3/5 bcoz if we take 1/2 + x/8 then x = 2 will be deleted bt we want x = 2 in our answer..]

Hence    P(2  <=  x  <  4)    =     1 - 0.6

                                          =    0.4

Hence required probability should be 0.40

Had it been P(2 < x < 4) , then it would have been 0.25 as in that case x = 2 would not be allowed hence it needed to be subtracted..

                                         

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