Why this Nondeterministic Finite accept this string?
When a transition doesn't exist for current (state, input) pair, the NFA halts and the computation path rejects the input string. Or if an empty string transition is defined, it can be used to go into a garbage state for undefined transitions and the computation path rejects the string. See What does an NFA do if there&#39;s no transition with the correct symbol? for really good information.

In addition, this source that says the string is not accepted: http://people.cs.nctu.edu.tw/~wgtzeng/courses/FL2013SpringUnder/2.%20Finite%20automata.pdf slide 15.