Answer:
False (under assumption T(2,-3) means move it right 2 units and down 3 units).
Explanation:
The statement is false.
T(2,-3) means move the point right 2 (so plus 2 on the x-coordinate) and down 3 units (so minus 3 on the y-coordinate).
So (1,6) will become (1+2,6-3)=(3,3) after the translation.
The point (1,12) will become (1+2,12-3)=(3,9).
If the statement were "Under the translation T(2,-3) the point (1,12) will become (3,9)", then it would be true.
Or!
If the statement were "Under the translation T(2,3) the point (1,6) will become (3,9)", then it would be true.