how do I modify makefile which is already compiled?

Let's say I have a makefile which looks like this:

all: a_functions.o b_functions.o c_functions.o d_functions.o main.o
     gcc -o all a_functions.o b_functions.o c_functions.o d_functions.o main.o
a_functions.o: a_functions.c
     gcc -c -o a_functions.o a_functions.c
b_functions.o: b_functions.c
     gcc -c -o b_functions.o b_functions.c
c_functions.o: c_functions.c
     gcc -c -o c_functions.o c_functions.c
main.o: main.c
     gcc -c -o main.o main.c

I could compile it using command

sudo make -f makefile

and program works nice if I run

./all

but how to do if I want to add for example a clean command in makefile? I added

clean:
     rm *.o all

at the end of the makefile but my terminal shows

-bash: ./clean: No such file or directory

when I do ./clean

Of course recompiling makefile doesn't work either. It shows

make: 'all' is up to date.

when I do sudo make -f makefile

I found here How to edit makefile? that you can use

$ CFLAGS="-std=c99" make

this command in terminal or I can add

CFLAGS=-std=c99

in my makefile but they still show

all is up to date

the image is just evidence that modifying did not work for me.