Áp dụng tính chất dãy tỉ số bằng nhau ta có
$\begin{align} & \frac{2020a+b+c+d}{a}=\frac{a+2020b+c+d}{b}=\frac{a+b+2020c+d}{c}=\frac{a+b+c+2020d}{d} \\ & =\frac{2023\left( a+b+c+d \right)}{a+b+c+d}=2023 \\ \end{align}$
Suy ra $\left\{ \begin{align} & 2020a+b+c+d=2023a \\ & a+2020b+c+d=2023b \\ & a+b+2020c+d=2023c \\ & a+b+c+2012d=2023d \\ \end{align} \right.$$\Rightarrow \left\{ \begin{align} & a+b+c+d=4a \\ & a+b+c+d=4b \\ & a+b+c+d=4c \\ & a+b+c+d=4d \\ \end{align} \right.$$\Rightarrow a=b=c=d$
Khi đó
$\begin{align} & M=\frac{a+b}{c+d}+\frac{b+c}{d+a}+\frac{c+d}{a+b}+\frac{d+a}{b+c} \\ & =\frac{a+a}{a+a}+\frac{b+b}{b+b}+\frac{c+c}{c+c}+\frac{d+d}{d+d} \\ & =1+1+1+1=4 \\ \end{align}$