4. 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 left 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 $d=$ $\qquad$.
4
4.【Analysis and Solution】For any real number $x$, we have $x * d=a x+c d+c d x=x_{1}$ (where $\left.d \neq 0\right)$,
$$
\begin{array}{l}
\therefore 0 * d=b d=0 . \\
\because d \neq 0, \quad \therefore b=0 .
\end{array}
$$

Thus, from $\left\{\begin{array}{l}1 * 2=a+2 b+2 c=3 \\ 2 * 3=2 a+3 b+6 c=4\end{array}\right.$,
we get $\left\{\begin{array}{l}a+2 c=3, \\ 2 a+6 c=4 .\end{array}\right.$
Therefore, $\left\{\begin{array}{l}a=5, \\ c=-1 .\end{array}\right.$
Also, from $1 * d=a+b d+c d=1$,

we get $d=4$.