The expression quantity negative 7 over 6 times t plus 4 over 9 end quantity minus expression quantity negative 5 over 12 times t plus 2 over 3 end quantity can be simplified as follows:
= (-7/6)t + (4/9) - (-5/12)t - (2/3)
= (-7/6 + 5/12)t + (4/9 - 2/3)
= (-21 + 10)/12t + (2 - 4)/9
= -11/12t - 2/9
= -(11/12)t - (2/9)
Therefore, the expression is equivalent to -(11/12)t - (2/9).