Today I was solving this question: The high temperature on April 4 was $6$ $C^\circ$ The high temperature on April 5 was $-2C^\circ$ What was the difference in temperatures?
And my teacher said the answer is -8 but I think it is +8. Who is right?why?
On
Either answer can be right. It depends on the context.
In a math class the official definition of "difference", which is what your teacher wants, is
$$
\text{recent value} - \text{older value} = (-2) - (6) = -8.
$$
I hope there was some discussion of this in class before you were asked the question.
You are thinking about the absolute value. In everyday language it would be perfectly reasonable to say "It was $8$ degrees colder on April $5$th than the day before." It would be a somewhat pedantic, but correct, to say "The April $5$th temperature changed $-8$ degrees from the day before."
The difference in temperature will be $$\Delta \rm T= T_{final}-T_{initial}=(-2)-(6)=-8$$
The "-" sign shows that there is decrease in the value of temperature.
Though, absolute difference will be $8$.