-2.4/-.15

Let's make this a fractional division problem. 

Simplify -15/100 to -3/20

${-12\over5}/{-3\over20}$

Flip the second fraction and change to multiplication.

${-12\over5}*{-20\over3}$

Multiply the numerators by each other and the denominators by each other.

${-12\over5}*{-20\over3}={240\over15}$

240/15 = 16, so ${-12\over5}/{-3\over20}=16$

So what you have is -2.4/-0.15.
Let's remove the minuses for the h**l of it. It's legit:
2.4/0.15
Now, when we divide by one, we get exactly the number on top. If we divide by one that's bigger than one, the result will be smaller than the result on top, and if we divide by one smaller than one, the result will be bigger than the number on top. I say that to make you believe there might be reason behind the madness.
Once that's said: It's hellish to divide by a number smaller than one. It's easier to multiply. We can do that if we rewrite 0.15 as a fraction. 1/1/2 (one divided by a half) can be rewritten as 2*1/1, for example. the logic is: if half a person gets one pie, an entire person gets two. As a general rule: x/y/z = x*z/y. We're gonna use that by rewriting 0.15 as a fraction.

I'm scared of writing too much, so long story short: 0.15 as a fraction is 3/20.
So instead of 2.4/0.15,
we have 2.4/3/20, (ew, division)
which can be rewritten as 2.4*20/3. (yay, multiplication)
That's 48/3, and that is - you know it - 16.