How many possible ways are there?
Say you want to pick, out of a multiset $S$, the numbers $x_1$, $x_2$, ..., $x_n$ with multiplicity $m_1$, $m_2$, ..., $m_n$  (i.e., you want to pick $x_1$ exactly $m_1$ times).
Furthermore, assume that in $S$ the numbers  $x_1$, $x_2$, ..., $x_n$ have multiplicity $s_1$, $s_2$,..., $s_n$.  (we assume for every $i$, $s_i \ge m_i$, otherwise no solution exists).

Consider the first element $x_1$: 
you have exactly $s_1 \choose m_1$ different ways to pick $m_1$ occurrences of $x_1$ from the $s_1$ times it appears in $S$.

In a similar way for all the other elements,  the answer would be
$${s_1 \choose m_1} {s_2 \choose m_2} \cdots {s_n \choose m_n} = \prod_{i=1}^n {s_i \choose m_i}$$



For your example, set $x_1=6$, $x_2=5$, $x_3=4$, $x_4=2$. 
In the data set they appear with multiplicity $s_1=1$, $s_2=2$, $s_3=1$, $s_4=4$ and you want to have $m_1=1$ sixes, $m_2=2$ fivess, $m_3=1$ fours and $m_3=2$ twos, so the number of different options is
$$ {1 \choose 1} {2 \choose 2} {1 \choose 1}{4 \choose 2}  = 1 \cdot 1 \cdot 1 \cdot 6$$