so hmmm first off, let's use the decimal format of a percentage, thus, 6% is rather just 6/100 or 0.06, and 15% is just 15/100 or just 0.15 and so on
now [tex]\bf \begin{array}{lccclll}
&amount&concentration&
\begin{array}{llll}
concentrated\\
amount
\end{array}\\
&-----&-------&-------\\
\textit{6\% solution}&x&0.06&0.06x\\
\textit{15\% solution}&y&0.15&0.15y\\
-----&-----&-------&-------\\
mixture&100&0.10&10
\end{array}[/tex]
whatever "x" and "y" may be, we know they must add up to 100 ounces, thus
x + y = 100
and whatever the concentrated amounts in the solution are for each, they must add up to 10 oz, thus
0.06x + 0.15y = 10
thus [tex]\bf \begin{cases}
x+y=100\implies \boxed{y}=100-x\\
0.06x+0.15y=10\\
----------\\
0.06x+0.15\left( \boxed{100-x} \right)=10
\end{cases}[/tex]
solve for "x", to see how much of the 6% solution will be needed
what about "y"? well, y = 100 - x
