(a)
Given, $R_{1} = k\lbrack A\rbrack^{2}\lbrack B\rbrack$
Let concentration of B is changed by x times.
Then,
$R_{2} = k\lbrack A/2\rbrack^{2}\lbrack xB\rbrack$
$= k \times x/4\lbrack A\rbrack^{2}\lbrack B\rbrack$
$= x/4 \times k\lbrack A\rbrack^{2}\lbrack B\rbrack$
As $R_{2} = R_{1},thus\ x = 4$