For the reaction, 2A + B → products, when the concentration of A...

$2A + B \to C$

Initial ${r}_{1} = k{\left[A\right]}^{x}{\left[B\right]}^{y} = 0.3m / sec$ ...(i)

${r}_{2} = k{\left[2A\right]}^{x}{\left[2B\right]}^{y} = 2.4$ ...(ii)

${r}_{3} = k{\left[2A\right]}^{x}{\left[B\right]}^{y} = 0.6$ ...(iii)

From (i) $\div$ (iii)

${\left(\dfrac{1}{2}\right)}^{x}{\left(1\right)}^{y} = \dfrac{0.3}{0.6}$

${\left(\dfrac{1}{2}\right)}^{x} = \dfrac{1}{2}$

$x = 1$

(ii) $\div$ (iii)

$\dfrac{{r}_{2}}{{r}_{3}} = \dfrac{2.4}{0.6} = {\left(2\right)}^{y}$

$4 = {\left(2\right)}^{y}$

$y = 2$

The order of reaction w.r.t. $A = 1$ and w.r.t. $B = 2$

Total order of reaction $= 1 + 2 = 3$