How to calculate the intercept of an indifference curve in an Edgeworth box?
In an edgeworth box model the total amount of goods must be constant. In your problem this translates to

\begin{eqnarray}
x_{A_1} + x_{B_1} &amp;=&amp; \omega_{A_1} + \omega_{B_1} = 10 + 4 = 14 \tag{1}\\
x_{A_2} + x_{B_2} &amp;=&amp; \omega_{A_2} + \omega_{B_2} = 6 + 2 = 8 \tag{2}\\
\end{eqnarray}

So let's consider the first intercept

$$
(x_{A_1}, x_{A_2}) = (0, 38/5) \tag{3}
$$

which you properly derived. If you replace these values in Eq. (1) you get

$$
0 + x_{B_1} = 14 ~~~\Rightarrow~~~ x_{B_1} = 14 \tag{4}
$$

and if you replace in Eq. (2) you get

$$
\frac{38}{5} + x_{B_2} = 8 ~~~\Rightarrow~~~ x_{B_2} = \frac{2}{5} \tag{5}
$$

So there you have it

$$
(x_{A_1}, x_{A_2}) = (0,38/5), ~~~(x_{B_1}, x_{B_2}) = (14,2/5)
$$

You can do the same for the other intercept, I will leave that for you to complete