Solve the following equations for the specified variable or correct the student's work: a) 2m = 10t, solve for t. b) 2m - 4 = -10, correct the student's work.

To find $t$, we need to isolate $t$ on one side of the equation. We can do this by dividing both sides by 10.

$$2m = 10t$$ $$\frac{2m}{10} = \frac{10t}{10}$$ $$\frac{m}{5} = t$$

So, $t$ in terms of $m$ is:

$$t = \boxed{\frac{m}{5}}$$

The student attempted to solve the equation $2m - 4 = -10$.
First, add 4 to both sides of the equation to isolate the term with $m$.

$$2m - 4 = -10$$ $$2m = -10 + 4$$ $$2m = -6$$

Next, divide both sides by 2 to solve for $m$.

$$\frac{2m}{2} = \frac{-6}{2}$$ $$m = -3$$

The student made an arithmetic error when calculating $-10 + 4$, which should be $-6$, not 14.
The correct value for $m$ is $\boxed{-3}$.