To find the total change in the amount of water in the tank after 6 days, we first need to determine how much water decreases in one 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 periods there are in one day:
\[ \text{Number of 3-hour periods in a day} = \frac{24 \text{ hours}}{3 \text{ hours/period}} = 8 \text{ periods} \]
Now, we can calculate the total decrease in one day:
\[ \text{Total decrease in one day} = 10 \text{ gallons/period} \times 8 \text{ periods} = 80 \text{ gallons} \]
Next, we can find the total decrease over 6 days:
\[ \text{Total decrease over 6 days} = 80 \text{ gallons/day} \times 6 \text{ days} = 480 \text{ gallons} \]
Therefore, the total change in the amount of water in the tank after 6 days is 480 gallons.