Problem with connection
I have attached photo with my problem. I don't know how to create this kind of connection
It looks a bit like a pencil. Have you looked in the Library here for a pencil? You could download one and see exactly how it was created in the feature tree.
A transition from a hexagon to a circle would most often be done as a loft.
In the example you showed, it is a bit different. My guess is that it was a simple cylinder, then a cut was taken to produce a flat. The cut feature was then patterned about the cylindrical axis to produce the required number of flats.