There is a (a bit lengthy , not useful, but visual) way to multiply numbers.
Case-1 If we want to multiply two one digit numbers, say $4\times 5$, then we can see the answer as number of intersections in the following figure-
i.e. we can count number of points of intersections in the figure which are $4\times 5=20$.
So if we want to extend this motivation (multiplication using counting intersection points) to multiplication of a two digit number with a single digit number, say, $15\times 5$- we will have to draw $15$ parallel lines and then cut them by $5$ parallel lines, and count $75$ points of intersection.
Case-2- Now to multiply two $2$ digit numbers, we see that , say $15\times 23$ we can draw figure as -
It is explained as- Suppose we have to multiply $ab \times cd$ where $a,b,c,d \in \{1,2,3,4,5,6,7,8,9\}$. Then we draw a lines on the place whrere the single black line on bottom is in above figure and draw $b$ parallel lines on top of it, after some gap, where pink lines are in figure. Then $c$ lines are drawn cutting these previously drawn lines, like at the place, in left of figure where $2$ brown lines are and then $d$ lines parallel to these $c$ lines are drawn in place where green lines are in the figure. Now we count the no. of points of intersection inside three circles drawn in figure from right to left. If in the right most circle, we have upto $9$ points then it is our last digit of the answer, and if greater than $9$, say there are $ef$ points in right circle where $e$ and $f$ are single digits, then $f$ is the unit digit of product and we carry over $e$ to middle circle and count points in middle and add carry over,if any, and see whether we need to carry over again to left circle or not, and assign a digit to middle circle and then count in left circle and carry over, if any.
Now this multiplication is same as I always multiplies two digit numbers, like, the figure explains 
Both methods are same whether we draw figure or not, and second method, the one one without figure and counting is faster than the usual way most people multiply.
But my question is, is there such a way (somewhat faster, may be based on some counting arguments etc) to multiply two three digit number or more than two $2$ digit numbers, in a little faster way.
**P.S.- ** Here is a video of this drawing method, in case not clearly explained in the question