brainfuck, 79 bytes

-[>++>++>++<<<-----]>----.>++++++++++++.<-.>>+++.+++++.<<+++++.>+++.<---.>>---.

Try it online!

It's not the shortest brainfuck submission, that would be @Sp3000's answer, but frankly, I dont understand how his submission works anyways, and this was the best I could do.

Explanation:

The word "brainfuck" is 9 letters: b(98), r(114), a(97), i(105), n(110), f(102), u(117), c(99), and k(107) Splitting these up into three groups by similar ascii values gives us our tape:

[Initial Count Cell] , [ABCF Cell] , [RU Cell] , [IKN Cell]

By using three cells instead of one to print the ascii characters, we cut down the number of bytes needed by nearly half.

-[>++>++>++<<<-----]     Wrapped loop sets all three ascii cells to 102
>----.                   print 'b'
>++++++++++++.           print 'r'
<-.                      print 'a'
>>+++.                   print 'i'
+++++.                   print 'n'
<<+++++.                 print 'f'
>+++.                    print 'u'
<---.                    print 'c'
>>---.                   print 'k'

Credits: -2 bytes thanks to @ETHproductions

brainfuck, 79 bytes

-[>++>++>++<<<-----]>----.>++++++++++++.<-.>>+++.+++++.<<+++++.>+++.<---.>>---.

Try it online!

It's not the shortest brainfuck submission, that would be @Sp3000's answer, but frankly, I dont understand how his submission works anyways, and this was the best I could do.

Explanation:

The word "brainfuck" is 9 letters: b(98), r(114), a(97), i(105), n(110), f(102), u(117), c(99), and k(107) Splitting these up into three groups by similar ascii values gives us our tape:

[Initial Count Cell] , [ABCF Cell] , [RU Cell] , [IKN Cell]

By using three cells instead of one to print the ascii characters, we cut down the number of bytes needed by nearly half.

-[>++>++>++<<<-----]     Wrapped loop sets all three ascii cells to 102
>----.                   print 'b'
>++++++++++++.           print 'r'
<-.                      print 'a'
>>+++.                   print 'i'
+++++.                   print 'n'
<<+++++.                 print 'f'
>+++.                    print 'u'
<---.                    print 'c'
>>---.                   print 'k'

Output:

brainfuck

Credits: -2 bytes thanks to @ETHproductions

brainfuck, 81 bytes

-[>++>++>++<<<-----]>----.>++++++++++++.<-.>>+++.<----.>---.<+++++++.<++.>>+++++.

Try it online!

It's not the shortest brainfuck submission, that would be @Sp3000's answer, but frankly, I dont understand how his submission works anyways, and this was the best I could do.

Explanation:

The word "brainfuck" is 9 letters: b(98), r(114), a(97), i(105), n(110), f(102), u(117), c(99), and k(107) Splitting these up into three groups by closest ascii values gives us our tape:

[Initial Count Cell] , [ABC Cell] , [NRU Cell] , [FIK Cell]

By using three cells instead of one to print the ascii characters, we cut down the number of bytes needed by nearly half.

-[>++>++>++<<<-----]     Wrapped loop sets all three ascii cells to 102
>----.                   print 'b'
>++++++++++++.           print 'r'
<-.                      print 'a'
>>+++.                   print 'i'
<----.                   print 'n'
>---.                    print 'f'
<+++++++.                print 'u'
<++.                     print 'c'
>>+++++.                 print 'k'

brainfuck, 79 bytes

-[>++>++>++<<<-----]>----.>++++++++++++.<-.>>+++.+++++.<<+++++.>+++.<---.>>---.

Try it online!

It's not the shortest brainfuck submission, that would be @Sp3000's answer, but frankly, I dont understand how his submission works anyways, and this was the best I could do.

Explanation:

The word "brainfuck" is 9 letters: b(98), r(114), a(97), i(105), n(110), f(102), u(117), c(99), and k(107) Splitting these up into three groups by similar ascii values gives us our tape:

[Initial Count Cell] , [ABCF Cell] , [RU Cell] , [IKN Cell]

By using three cells instead of one to print the ascii characters, we cut down the number of bytes needed by nearly half.

-[>++>++>++<<<-----]     Wrapped loop sets all three ascii cells to 102
>----.                   print 'b'
>++++++++++++.           print 'r'
<-.                      print 'a'
>>+++.                   print 'i'
+++++.                   print 'n'
<<+++++.                 print 'f'
>+++.                    print 'u'
<---.                    print 'c'
>>---.                   print 'k'

Credits: -2 bytes thanks to @ETHproductions