Answer: No, it is impossible to make the square grid contains exactly 574 black units. Denote the move that changing the colours of all unit squares in row $n$ is $A_n$, the move that changing the colours of all unit squares in column $m$ is $B_m$. For any moves $C_1,C_2,\cdots,C_j\in\{A_1,A_2,\cdots,A_{24},B_{1},B_{2},\cdots,B_{24}\}$, We define $C_1C_2\cdots C_j$ as a series of step-by-step operations that we do the operations $C_1$, $C_2$, $\cdots$, $C_j$ in order. For any $m,n\in\{1,2,\cdots,24\}$, it is easy to know that $A_mA_n=A_nA_m$, $A_mB_n=B_nA_m$, $B_mB_n=B_nB_m$. Hence, for any series of operation $C_1C_2\cdots C_j$, it can be equivalent to $A_{i_1}A_{i_2}\cdots A_{i_p}B_{i_{p+1}}B_{i_{p+2}}\cdots B_{i_{j}}\ (1\leq i_1\leq i_2\leq\cdots\leq i_j)$ . Obviously, we can see that if there is a number $r$ satisfying $i_r=i_{r+1}$, then $A_{i_{r-1}}A_{i_r}A_{i_{r+1}}A_{i_{r+2}}$ can be simplified to $A_{i_{r-1}}A_{i_{r+2}}$ ($B$ also). So, after finitely many times, $A_{i_1}A_{i_2}\cdots A_{i_p}B_{i_{p+1}}B_{i_{p+2}}\cdots B_{i_{j}}$ can be simplified to $A_{i_1'}A_{i_2'}\cdots A_{i_q'}B_{i_{q+1}'}B_{i_{q+2}'}\cdots B_{i_k'}\ (i_1'<i_2'<\cdots<i_k')$. If the series of operations $A_{i_1'}A_{i_2'}\cdots A_{i_q'}B_{i_{q+1}'}B_{i_{q+2}'}\cdots B_{i_k'}$ can make the 576 white square grids become 574 black square grids, then we get \begin{align} 24q+24(k-q)-2q(k-q)&=574\notag\\ q(k-q)-12q-12(k-q)+287&=0\notag\\ (q-12)(k-q-12)&=-143 \end{align} But, $0\leq q,k-q\leq 24 \Leftrightarrow |q-12|,|k-q|\leq 12 \Rightarrow 13\nmid q-12\ \text{and}\ 13\nmid k-q-12\Rightarrow 13\nmid(q-12)(k-q-12)=-143$, contradiction.

We have 24×24=576 squares in the 24×24 square grid. We have to colour all squares black or white. Therefore,exactly 574 is not possible.

Banglarmanush wrote: We have 24×24=576 squares in the 24×24 square grid. We have to colour all squares black or white. Therefore,exactly 576 is not possible. what. that makes no sense. It is very easy to color all $576$ squares black; we go through each column and color it all black (or each row works too). The goal here is to make $574$ squares black and $2$ white. This adds to $576,$ which is the total number of squares.

Ok,I am adding some another things here.Sorry bro I am late. Take, A row and colour it black And repeat it until the last Now,we have 576 black unit squares. Take, A row and colour it white 576-24=552 squares We can see that, it is never possible to have exactly 574 black squares is not possible.