Here,

Since, $\frac{2}{3}$ of students received A in the class as whole, so $\frac{1}{3}$ of students received A in final but not in class as whole and they are = 15 students

25 % received A on final exam

Let the total number of student = x

we can re-write the equation as -

$\frac{1}{4 }* \frac{1}{3} * x = 15$

or $x = 180$

Since 25% received A , therefore 75% didnot received A ,

i.e = $\frac{3}{4}$ * 180 = 135

SECOND METHOD: -

Let pick an answer from the given answer, (we can start for C or D and move up or down accordingly)

Let us choose C, which is = 105 ( total number of students didn't received A)

i.e $\frac{3}{4 } x = 105$

or $x = 140$

25% of 140 = 35

and $\frac{2}{3 } * 35 = \frac{70}{3}$

check {$35 - (\frac{75}{3})$} < 15 students , which donot match as per the information provided in question. Hence option C is not our answer ( also note 35 - 75/ 3 = almost 11, so we move down to option D)

so we need to move to option D, which is 135 students

now,
$\frac{3}{4 } * x = 135$

or x = 180

25% of 180 = 45

and $\frac{2}{3} * 45 = 30$

check 45 - 30 = 15 students students in the class received A’s on the final exam but did not receive an A in the class ( which is given )

Hence option D is our answer