Answer
$$(0,0)=\frac{1}{2}t(2,4)+t(-1,-2)+0(0,6).$$
$$(-1,-2)=-\frac{1}{2}(2,4)+0(0,6) .$$
Work Step by Step
Consider the combination
$$a(2,4)+b(-1,-2)+c(0,6) =0, \quad a,b,c \in R.$$
Which yields the following system of equations
\begin{align*}
2a-b &=0\\
4a-2b+6c &=0.
\end{align*}
The augmented matrix matrix is given by
$$\left[\begin {array}{cccc} 2&-1&0\\ 4&-2&6
\end {array}
\right]$$
The reduced row echelon form can be calculated as follows
$$\left[\begin {array}{cccc}1&-\frac{1}{2}&0\\ 0&0&1
\end {array}
\right],$$
then we have the solution
$$a=\frac{1}{2}t,\quad b= t, \quad c=0.$$
Hence, we have the combinations
$$(0,0)=\frac{1}{2}t(2,4)+t(-1,-2)+0(0,6).$$
$$(-1,-2)=-\frac{1}{2}(2,4)+0(0,6) .$$
