How do I write 7t+7/-6 divided by 4t+4/15 in lowest terms ?

I will assume you mean

(7t+7)/-6 divided by (4t+4)/15

= (7(t+1)/-6 ) ÷ ( 4(t+1)/15)
= 7(t+1)/-6 * (15/(4(t+1))
= -35/8