Comparing DES and DES-X variation: $Enc(m) = DES_{k_1}(m \oplus k_2)$
The hint that you have given is simply saying that, if you have more than one (better many) plaintext-ciphertext pairs;


First, apply the n-pad attack to recover the real $k_2$ by;
$$p_1 \oplus p_2 = m_1 \oplus m_2$$
$$p_1 \oplus p_3 = m_1 \oplus m_3,\ldots$$etc. Once you recover one of the $m_i$'s than $$ p_i = k_2 \oplus m_i$$ is enough to extract the $k_2$ 
Then apply the usual brute-force with $k_2$ is known.


Note: your DES-X is not using key whitening which uses 3 keys, not 2.