2. For real numbers $x, y$, define a new operation $x: y=a: c+b y+$ $c x y$. Here $a, b, c$ are constants, and the usual operations are addition and multiplication, with $1 \times 2=: 3,2 \times 3=4$, and there exists a non-zero constant $d$, such that for any $x$, we have $x$ * $d=x$. Then the value of $d$ is ( ).
(A) 3
(B) 4
(C) 5
(D) 6
2. B.

Solution $1 * 2=3 \Rightarrow a+2 b+2 c=3$,
$2 * 3=4 \Rightarrow 2 a+3 b+6 c=4$,
$x * d=x \Rightarrow a x+b d+c d x=x$.
Let $x=0$, then we have $b d=0, d \neq 0, b=0$.
$\Rightarrow\left\{\begin{array}{l}a+2 c=3, \\ a+3 c=2\end{array} \Rightarrow a=5, c=-1\right.$.
Let $x=1$. Substituting into (3) we get
$$
5+(-1) \cdot d \cdot 1=1, d=4
$$