##05AB1E, 14 10 bytes##

Code:

|vyþyyþ-¶J

Explanation:

|                 # push all lines in input as array of strings
 v                # for each line in array
  yþ              # push only digits from line
    yyþ-          # push line without digits
        ¶         # push newline char
         J        # join as string
                  # end loop and print explicitly

Example Input:

A word can have any number of text like 433884,
but all the numb89ers has to be moved left side
but alph6abetical va9lues has to be pas46ted on right side.
The text might con4tain chara29cters s2huffled like hlep or dfeintino or even
meaningless words co43mbined togeth81er.

Example Output:

433884A word can have any number of text like ,
89but all the numbers has to be moved left side
6946but alphabetical values has to be pasted on right side.
4292The text might contain characters shuffled like hlep or dfeintino or even
4381meaningless words combined together.

Try it online

05AB1E, 14 10 bytes

Code:

|vyþyyþ-¶J

Explanation:

|                 # push all lines in input as array of strings
 v                # for each line in array
  yþ              # push only digits from line
    yyþ-          # push line without digits
        ¶         # push newline char
         J        # join as string
                  # end loop and print explicitly

Example Input:

A word can have any number of text like 433884,
but all the numb89ers has to be moved left side
but alph6abetical va9lues has to be pas46ted on right side.
The text might con4tain chara29cters s2huffled like hlep or dfeintino or even
meaningless words co43mbined togeth81er.

Example Output:

433884A word can have any number of text like ,
89but all the numbers has to be moved left side
6946but alphabetical values has to be pasted on right side.
4292The text might contain characters shuffled like hlep or dfeintino or even
4381meaningless words combined together.

Try it online

##05AB1E, 14 bytes##

Code:

|vyþyyþ-¶J})€,

Will add explanation after I've tried golfing it some.

Example Input:

A word can have any number of text like 433884,
but all the numb89ers has to be moved left side
but alph6abetical va9lues has to be pas46ted on right side.
The text might con4tain chara29cters s2huffled like hlep or dfeintino or even
meaningless words co43mbined togeth81er.

Example Output:

433884A word can have any number of text like ,
89but all the numbers has to be moved left side
6946but alphabetical values has to be pasted on right side.
4292The text might contain characters shuffled like hlep or dfeintino or even
4381meaningless words combined together.

##05AB1E, 14 10 bytes##

Code:

|vyþyyþ-¶J

Explanation:

|                 # push all lines in input as array of strings
 v                # for each line in array
  yþ              # push only digits from line
    yyþ-          # push line without digits
        ¶         # push newline char
         J        # join as string
                  # end loop and print explicitly

Example Input:

A word can have any number of text like 433884,
but all the numb89ers has to be moved left side
but alph6abetical va9lues has to be pas46ted on right side.
The text might con4tain chara29cters s2huffled like hlep or dfeintino or even
meaningless words co43mbined togeth81er.

Example Output:

433884A word can have any number of text like ,
89but all the numbers has to be moved left side
6946but alphabetical values has to be pasted on right side.
4292The text might contain characters shuffled like hlep or dfeintino or even
4381meaningless words combined together.

Try it online