Why my Python function is not returning any value?

As the previous answers have pointed out, you are not saving the return value of the main_menu() function anywhere. But you also have a few other errors in your code, so let's address those first.

1. You need to define your function before you can use it. You seem to be trying to call the add_number function and define it at the same time. First define your function, and then call it something like so:

# Define the add_number() function
def add_number():
    clean()
    ...

if main == 1:
    # call the add_number() function
    add_number()
    

2. You are trying to iterate a number, which will throw an error. You can try and use the range function for this instead.

number = int(input("----->"))
for i in range(number): # using range function
   ...

3. You are trying to convert the name to an int, but I assume you probably want it to be a string.

# this will throw an ValueError if you type a name like "John"
c_n = int(input("Name-->")) 

# This will not throw an error because you are not converting a string into an int
c_n = input("Name-->")

4. Your try block is catching SyntaxErrors, but your probably want to catch ValueErrors. A syntax error is an error in your code syntax, like forgetting a : or something. While a value error is an error that is produced when some date is of the wrong value, like when you trying and convert a string to an int.

# replace SyntaxError with ValueError
except ValueError:
    print("Oops something went wrong!")

5. Finally if you want to go back to the menu after you enter your contact numbers, you will need some kind of loop.

while(True):
    # here we are saving the return value main_menu() function
    choice = main_menu()
    if choice == 1:
        add_number()

    # add other options here

    else:
      print("Sorry that option is not available")

This loop will show the main_menu and ask the user for an option. Then if the user chooses 1 it will run the add_number() function. Once that function is done, the loop will start over and show the menu.

All together that looks like this:

import pandas as pd
#list for containing telephone number
telephone = []
#list containing contact name
contact_name = []

def main_menu():
    intro = """ ----------------------WElCOME to MyPhone-----------------------
    To select the task please type the number corrosponding to it
    1)Add New Number
    2)Remove Contact
    3)Access old contact
    ----> """
    main = int(input(intro))
    return main

def clean():
    print("--------------------------------------------------------------------------------------")

def add_number():
    clean()
    try:
        print("How many number(s) you want to add. Remember if you don't want to add any number just click enter",end="")
        number = int(input("----->"))
        for i in range(number):
            c_n = input("Name-->")
            t_n = int(input("Number-->"))
            contact_name.append(c_n)
            telephone.append(t_n)
        else:
            print("Contacts are Saved!👍")
    except ValueError:
        print("Oops something went wrong!")

while(True):
    choice = main_menu()
    if choice == 1:
        add_number()
    # add other options here

    # catch any other options input
    else:
      print("Sorry that option is not available")