{Through the wall} (dia tou teichous). Paul in  2Co 11:33 
explains dia tou teichous as being dia thuridos (through a
window) which opened into the house on the inside of the wall as
is true today in Damascus as Hackett saw there. See  Jos 2:15f. 
(cf.  1Sa 19:12 ) for the way that Rahab let out the spies "by a
cord through the window." {Lowering him} (auton chalasantes).
First aorist active participle of chala(935c), old and common verb
in a nautical sense ( Ac 27:17,30 ) as well as otherwise as here.
Same verb used by Paul of this experience ( 2Co 11:33 ). {In a
basket} (en sphuridi). The word used when the four thousand
were fed ( Mr 8:8  Mt 15:37 ). A large basket plaited of reeds
and distinguished in  Mr 8:19f.  ( Mt 16:9f. ) from the smaller
kophinos. Paul uses sargan(885c), a basket made of ropes. This
escape by night by the help of the men whom he had come to
destroy was a shameful memory to Paul ( 2Co 11:33 ). Wendt thinks
that the coincidences in language here prove that Luke had read
II Corinthians. That, of course, is quite possible.