Multiplying by -1 can be considered as being the operation that "reverses the direction" of the line, a bit like reflecting it in the zero point.
Let's work towards -3 x -2.
To start with, we'll consider 3 x 2. Easy enough, that's 6. You can, if you like, think of the number line as a piece of elastic, with a dot at the 3 point. Multiplying by 2 is like stretching the elastic to twice its length. The 3 ends up being where 6 was. Thus we illustrate 2x 3 = 6.
Now take 2 x -3. Same piece of elastic, this time the dot is at the -3 point. Stretch it to twice its length, but this time imagine it being pulled from the opposite end as well, so the negative numbers get stretched as well. The -3 ends up where the -6 was.
Now take -2 x 3. You start with the dot at the 3 point, but this time not only do you stretch the elastic to twice its length, you pull the right hand end with your left hand and the left hand end with your right hand. So the entire piece of elastic "swaps ends" before being stretched, and the 3, having been swapped with -3, then gets stretched so it now lies on the -6.
Now take -2 x -3. Same thing, except the dot is at the -3 point, and when it swaps ends, it ends up at 3 before being stretched to 6.
The idea of "reversing direction" is a useful one for imagining what "multiplication by a negative number" is, it's like "multiply by its positive value, then change its sign."
When you get onto some applications in which negative number multiplication is actually used for something real-world, it will start to make proper sense, believe me - till then it's all this picturesque imaginings about elastic.
Let me know if it doesn't make sense. Point out the first line where I've lost you if not, and I'll try and make it clearer. (Might not be tonight, it's almost 11 where I am and it's a work day tomorrow and I'm *tired*!)
All the best - keep the faith!