10. For any real numbers $x, y$, define the operation $x * y$ as $x * y=a x+b y+c x y$, where $a, b, c$ are constants, and the operations on the right side of the equation are the usual real number addition and multiplication. It is known that $1 * 2=3, 2 * 3=4$, and there is a non-zero real number $d$, such that for any real number $x$ we have $x * d=x$, then $d=$ $\qquad$
$$
\begin{array}{l}
x * d=a x+b d+c d x=x \Rightarrow\left\{\begin{array} { l } 
{ a + c d = 1 , } \\
{ b d = 0 ( d \neq 0 ) , }
\end{array} \Rightarrow \left\{\begin{array}{l}
a+c d=1, \\
b=0 .
\end{array}\right.\right. \\
\text { Therefore }\left\{\begin{array} { l } 
{ 1 * 2 = a + 2 b + 2 c = 3 , } \\
{ 2 * 3 = 2 a + 3 b + 6 c = 4 , }
\end{array} \Rightarrow \left\{\begin{array} { l } 
{ a + 2 c = 3 , } \\
{ a + 3 c = 2 , }
\end{array} \Rightarrow \left\{\begin{array}{l}
a=5, \\
c=-1,
\end{array} \Rightarrow d=4 .\right.\right.\right.
\end{array}
$$