In \[\vartriangle \text{ }APQ\text{ }and\vartriangle \text{ }ABC\]
\[\angle APQ\text{ }=\angle ABC\]
[As PQ || BC, corresponding angles are equal.]
\[\angle PAQ\text{ }=\angle BAC\]
[Common angle]
Hence, \[\vartriangle APQ\text{ }\sim\text{ }\vartriangle ABC\text{ }by\text{ }AA\] criterion for similarity
So, we have
\[AP/AB\text{ }=\text{ }AQ/AC\]
\[AP/9\text{ }=\text{ }4.2/6\]
Hence,
\[AP\text{ }=\text{ }6.3\text{ }cm\]