The incorrect equation is:
(A) $ {(\Lambda _m^0)_{KCl}} - {(\Lambda _m^0)_{NaCl}} = {(\Lambda _m^0)_{KBr}} - {(\Lambda _m^0)_{NaBr}} $
(B) $ {(\Lambda _m^0)_{NaBr}} - {(\Lambda _m^0)_{NaI}} = {(\Lambda _m^0)_{KBr}} - {(\Lambda _m^0)_{NaBr}} $
(C) $ {(\Lambda _m^0)_{{H_2}O}} = {(\Lambda _m^0)_{HCl}} + {(\Lambda _m^0)_{NaOH}} - {(\Lambda _m^0)_{NaCl}} $
(D) $ {(\Lambda _m^0)_{NaBr}} - {(\Lambda _m^0)_{NaCl}} = {(\Lambda _m^0)_{KBr}} - {(\Lambda _m^0)_{KCl}} $

Hint: The molar conductivity of an electrolyte is represented by $ \Lambda _m^0 $ . It is defined as the sum of molar ionic conductance of its ions each multiplied by the number of a number of such ions present in one formula unit of electrolyte. If the left-hand side and the right-hand side of the equation are not equal then the equation will be incorrect.
Formula used
Molar conductivity, $ {\left( {\Lambda _m^0} \right)_{AB}} = {\left( {\Lambda _m^0} \right)_{{A^ + }}} - {\left( {\Lambda _m^0} \right)_{{B^ - }}} $
Where, $ \Lambda _m^0 $ is the molar conductivity of an electrolyte, $ {\left( {\Lambda _m^0} \right)_{{A^ + }}} $ is the molar ionic conductance of $ {A^ + } $ ions, and $ {\left( {\Lambda _m^0} \right)_{{B^ - }}} $ is the molar ionic conductance of $ {B^ - } $ ion.

Complete step by step answer:
Now we are ready to answer the question, we have the basic knowledge of the molar conductivity of an electrolyte. So, now we will check the given equations by solving the left-hand side and the right-hand side of the equation. So let’s start.
The equation which we are considering here is $ {(\Lambda _m^0)_{NaBr}} - {(\Lambda _m^0)_{NaI}} = {(\Lambda _m^0)_{KBr}} - {(\Lambda _m^0)_{NaBr}} $ . Now we will use the basic molar conductance of an electrolyte. Now we will solve the left-hand side as well as the right-hand side part of the equation and compare them.
 $ {(\Lambda _m^0)_{NaBr}} - {(\Lambda _m^0)_{NaI}} = {(\Lambda _m^0)_{KBr}} - {(\Lambda _m^0)_{NaBr}} $
 $ {(\Lambda _m^0)_{N{a^ + }}} + {(\Lambda _m^0)_{B{r^ - }}} - {(\Lambda _m^0)_{N{a^ + }}} - {(\Lambda _m^0)_{{I^ - }}} = {(\Lambda _m^0)_{{K^ + }}} + {(\Lambda _m^0)_{B{r^ - }}} - {(\Lambda _m^0)_{N{a^ + }}} - {(\Lambda _m^0)_{B{r^ - }}} $
Here, we have used the basic formula of molar ionic conductance as the sum of individual ions. Now we will use basic mathematics to solve the equation.
 $ {(\Lambda _m^0)_{B{r^ - }}} - {(\Lambda _m^0)_{{I^ - }}} = {(\Lambda _m^0)_{{K^ + }}} - {(\Lambda _m^0)_{N{a^ + }}} $
From the above equation, we can observe that the left-hand side and the right-hand side part of the equation are not equal. Hence, the equation is incorrect.
Therefore, the correct option is (B).

Note:
The above equations and the formula of molar ionic conductance are based upon the exhaustive experimental studies of the great scientist Kohlrausch. He gave the generalization on the contribution of one mole of ions which is known as Kohlrausch’s law.