B

设$BP=x$，则$AP=AB-BP=7-x$，
$\because \widehat {BD}=\widehat {BD}$，
$\therefore \angle A=\angle C$，
又$\because \angle APD=\angle CPB$，
$\therefore \triangle ADP$∽$\triangle CBP$，
$\therefore \frac{AP}{CP}=\frac{DP}{BP}$，即$\frac{7-x}{2}=\frac{6}{x}$，
$\therefore x\left(7-x\right)=12$，
解得$x_{1}=3$，$x_{2}=4$，
$\therefore PB$的长为$4$或$3$.
故选：$B$.