Yes,this question can be solved by finding molar mass first by using the formula of density and then finding number of atoms by unitary method. Both the method would be more appropriate (the given one or by finding mass) depending on you whether you are able to understand it or not.
In NCERT this question is solved by finding first the number of unit cell present in 208 gm of the elements which can be calculated by dividing the volume occupied by 208 gm of the elements by the volume of each unit cell.
Volume of the unit cell = (288 pm)3
= (288×10-10 cm)3
= 2.39×10-23 cm3
Volume of 208 g of the element = mass / density
= 208 / 7.2 = 28.88 cm3
Number of unit cells in this volume = 28.88 / 2.39 x 10?23
= 12.08×1023 unit cells
Then, in each unit cell of bcc two atoms are present. Therfore for obtaining the number of atoms in number of unit cells is multiply by 2.
Since each bcc cubic unit cell contains 2 atoms, therefore, the total number of atoms in 208 g = 2 × 12.08 × 1023 unit cells
= 24.16×1023 atoms