\(-11\dfrac{3}{4}-\left(6\dfrac{5}{6}-4\dfrac{1}{2}\right)-1\dfrac{2}{3}\)
\(=-\dfrac{47}{4}-\left(\dfrac{41}{6}-\dfrac{9}{2}\right)-\dfrac{5}{3}\)
\(=-\dfrac{47}{4}-\dfrac{41}{6}+\dfrac{9}{2}-\dfrac{5}{3}\)
\(=\left(-\dfrac{47}{4}+\dfrac{9}{2}\right)-\left(\dfrac{41}{6}+\dfrac{5}{3}\right)\)
\(=-\dfrac{29}{4}-\dfrac{17}{2}\)
\(=-\dfrac{63}{4}\)