To calculate the total change in the amount of water in the tank after 6 days, we first determine the rate of decrease in gallons per day.
The tank decreases by 10 gallons every 3 hours. There are 24 hours in a day, so we can find out how many 3-hour intervals are in a day:
\[ \text{Number of 3-hour intervals in a day} = \frac{24 \text{ hours}}{3 \text{ hours}} = 8 \text{ intervals} \]
Next, we calculate the total decrease in gallons per day:
\[ \text{Decrease per day} = 10 \text{ gallons/interval} \times 8 \text{ intervals/day} = 80 \text{ gallons/day} \]
Now, we find the total decrease over 6 days:
\[ \text{Total decrease after 6 days} = 80 \text{ gallons/day} \times 6 \text{ days} = 480 \text{ gallons} \]
Thus, the total change in the amount of water in the tank after 6 days is 480 gallons.