For left loop $BCFAB,$ $4 I_{1}+2 I_{1}=30-6$ or $6 I_{1}=24 \Rightarrow I_{1}=4 A$

In this equation on $I_{2}$ term so the current flowing in the left loop is independent of the right loop.

For right loop $DCFED,$ $1 I_{2}+2 I_{2}=15-6$ or $3 I_{2}=9 \Rightarrow I_{2}=3 A$

Here also no $I_{1}$ term so The current flowing in the right loop is independent of the left loop.

Net current in through $6 \mathrm{V}$ battery is: $I=I_{1}+I_{2}=4+3=7 \mathrm{A}$

Thus, the $6 \mathrm{V}$ battery is getting charged. Both $15 \mathrm{V}$ and $30 \mathrm{V}$ batteries produce current in $6 V$ battery.