To find the total change in the amount of water in the tank after 6 days, we first calculate how much the tank decreases in one day.
The tank decreases by 10 gallons every 3 hours. There are 24 hours in a day, so we can calculate the number of 3-hour periods in one day:
\[ \text{Number of 3-hour periods in one day} = \frac{24 \text{ hours}}{3 \text{ hours/period}} = 8 \text{ periods} \]
Next, we find the total decrease in gallons for one day:
\[ \text{Decrease per day} = 10 \text{ gallons/period} \times 8 \text{ periods} = 80 \text{ gallons} \]
Now, to find the total decrease over 6 days:
\[ \text{Total decrease after 6 days} = 80 \text{ gallons/day} \times 6 \text{ days} = 480 \text{ gallons} \]
Since the tank is decreasing in water, we express our answer as a negative change:
\[ \text{Total change} = -480 \text{ gallons} \]
Thus, the final answer is:
−480 gallons.