[tex]\it |\overrightarrow{AC}+\overrightarrow{BD}|=|\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{BA}+\overrightarrow{AD}|=|\ -\overrightarrow{BA}+\overrightarrow{BC}+\overrightarrow{BA}+\overrightarrow{AD}|=\\ \\ \\ =|\overrightarrow{BC}+\overrightarrow{AD}|=|\overrightarrow{BC}+2\overrightarrow{BC}|=|3\overrightarrow{BC}|=3|\overrightarrow{BC}|=3\cdot4=12[/tex]