Actually in the previous semester I have also made some Tkinter application which is the project given by teacher to us. So I go to some tutorials website of Python and find three methods of placing the widgets on the output screen. The three methods are

 1. Pack()
 2. Grid()
 3. Place() #the best method over Pack() and Grid()

Place() method take the coordinates in the form of the x and y. See this link for more clarification https://www.tutorialspoint.com/python/python_gui_programming.htm

https://www.tutorialspoint.com/python/tk_place.htm

See the bottom of the Page of the given link.The Place() method is defined with its proper arguments. I will prefer the Place() method over Pack() and Grid() because it works like CSS as we use in html, because it take the value of (width,height) and place your widget according to wherever you want.

If you find your answer a thumbs up will be appreciated.

Causing a widget to appear requires that you position it using with what Tkinter calls "geometry managers". The three managers are grid, pack and place. Each has strengths and weaknesses. These three managers are implemented as methods on all widgets.

grid, as its name implies, is perfect for laying widgets in a grid. You can specify rows and columns, row and column spans, padding, etc.

Example:

b = Button(...)
b.grid(row=2, column=3, columnspan=2)

pack uses a box metaphor, letting you "pack" widgets along one of the sides of a container. pack is extremely good at all-vertical or all-horizontal layouts. Toolbars, for example, where widgets are aligned in a horizontal line, are a good place to use pack.

Example:

b = Button(...)
b.pack(side="top", fill='both', expand=True, padx=4, pady=4)`

place is the least used geometry manager. With place you specify the exact x/y location and exact width/height for a widget. It has some nice features such as being able to use either absolute or relative coordinates (for example: you can place a widget at 10,10, or at 50% of the widgets width or height).

Unlike grid and pack, using place does not cause the parent widget to expand or collapse to fit all of the widgets that have been placed inside.

Example:

b = Button(...)
b.place(relx=.5, rely=.5, anchor="c")

With those three geometry managers you can do just about any type of layout you can imagine.

So I would like the "next set" and "exit" buttons to switch spots.

The packer works by placing widgets along one of the sides of the unallocated space in the master widget. Order matters, since each widget causes the unallocated space to change. For example, if you want a widget on the far right side of a frame, you should pack it on the right before you pack any other widgets.

In your case, the solution is as simple as changing the order in which you call pack.

tk.Button(fram, text="  Exit  ", command=self.destroy, fg = "grey").pack(side=tk.RIGHT)
tk.Button(fram, text="            Next set              ", command=self._load_dataset).pack(side=tk.RIGHT)

I was also wondering if it was possible to show the exit button on the bottom right of the screen.

Yes, it's possible. The simplest solution is to divide your window into three areas: a top set of buttons, a buttom set of buttons, and the image area.

For example, the following code creates three frames for these three areas, and uses pack to arrange them. Once you do these, it becomes trivial to add buttons to the top and bottom frames in whatever order you want.

top_frame = tk.Frame(self)
bottom_frame = tk.Frame(self)
image_frame = tk.Frame(self)

top_frame.pack(side="top", fill="x")
bottom_frame.pack(side="bottom", fill="x")
image_frame.pack(side="top", fill="both", expand=True)

exit_button = tk.Button(bottom_frame, text="Exit", ...)
exit_button.pack(side="right")

previous_button = tk.Button(top_frame, text="Previous Image", ...)
next_button = tk.Button(top_frame, text="Next Image", ...)
next_set_button = tk.Button(top_frame, text="Next Set", ...)

previous_button.pack(side="left")
next_button.pack(side="left")
next_set_button.pack(side="right")

Another way to do this is to make all of the buttons a child of self which makes it easy to define them all in the same block of code, and use the in_ parameter to specify where they go.

exit_button = tk.Button(self, text="Exit", ...)
previous_button = tk.Button(self, text="Previous Image", ...)
next_button = tk.Button(self, text="Next Image", ...)
next_set_button = tk.Button(self, text="Next Set", ...)

exit_button.pack(in_=bottom_frame, side="right")
previous_button.pack(in_=top_frame, side="left")
next_button.pack(in_=top_frame, side="left")
next_set_button.pack(in_=top_frame, side="right")

For the definitive description of how the packer works, see Packer Algorithm in the official tk documentation.