2. Given the system of inequalities about $x$
$$
\left\{\begin{array}{l}
2 x-1>3, \\
4 x-2 \geqslant a
\end{array}\right.
$$

the solution set is $x>b$. Then the value of the expression
$$
|a-3 b|-2|a-4 b|
$$

is ( ).
(A) $3 a-11 b$
(B) $5 b-a$
(C) $22-3 a$
(D) $a-10$
2. D.

From the given inequality, we get $x>2, x \geqslant \frac{a+2}{4}$.
From the problem, we get $\frac{a+2}{4} \leqslant 2, b=2$.
Then $a \leqslant 6 \leqslant 3 b<4 b$.
Thus $|a-3 b|-2|a-4 b|$
$$
\begin{array}{l}
=(3 b-a)-2(4 b-a) \\
=a-5 b=a-10 .
\end{array}
$$