We are going to Select the cylinder with Left-Click that you want to parent to the empty axis. You can select multiple objects by holding down the Shift key while clicking on each object.
Shift-select the empty axis object to make it the active object. The active object is the last object selected and will be the parent of the other selected objects.
Press Ctrl + P on your keyboard to bring up the Parent menu.
From the Parent menu, select Object to parent the selected objects to the empty axis.
The selected objects will now be parented to the empty axis. You can verify this by moving or rotating the empty axis, and the child objects will follow along.