How to return an object like TH1F*[][]?

Try with:

std::vector<std::vector<TH1F*> > ArrayManager::myHisto() {
  std::vector<std::vector<TH1F*> > histo(2, std::vector<TH1F*>(3));
  // ...
  return histo;
}

or maybe even better:

std::vector<std::vector<TH1F*> > *ArrayManager::myHisto() {
  std::vector<std::vector<TH1F*> > *histo = 
    new std::vector<std::vector<TH1F*> >(2, std::vector<TH1F*>(3));
  // ...
  return histo;
}

BTW. When you post “source code” or “output” here, do remember to enclose them into two lines which contain just three characters ``` (see how your posts have been edited above).