possible to decrypt RSA using these parameters only? If our message is 204, our public RSA-key is (e, N) = (47, 221) but the private key is unknown.
is it possible to retrieve the message without the private key and what would be the steps to do so?

In this case the rather obscure cycle attack works very well, by coincidence (or not; it's an exercise after all, with small parameters)
This works as follows: 
suppose the public key is $(N,e)$ and we receive the message $c$.
Then compute $c_0 = c, c_{n+1} = c^e \pmod{N}$ until $c = c_k$ for some $k \ge 1$ (this will always happen, only normally $k$ will be very large, but with small parameters its doable). Then $c_{k-1}$ is the original message (as its encryption is $c_k =c$).
Doing it here already gives $c_2 = 204$ and $c_1 = 68$ which is the plaintext.
This paper explains why this is normally not a realistic attack in practice .
