The equation can represents this situation is $$4x-2=22$$,  so, $$4x=24$$, $$x=6$$.  So, the answer is $$6$$. 
Jack\textquotesingle s sister is $$22$$ years old, which is $$2$$ less than $$4$$ times Jack\textquotesingle s age. Assume Jack is $$x$$ years old, then． 

1) $$x=4$$ 
2) $$x=5$$ 
3) $$x=6$$ 
4) $$x=8$$ 