I got it! The red line is based off the number 1. The blue line is based off the number 3. To get the next part, take the total amount of all the lines that connect to the black lines, including the black lines. This equals 6 in this case. Then, take the total amount of all the lines that connect with the green line, including the green line. This equals 5 in this case. The red line gives you the final number.

This is pretty cool. For those confused, it is just a visual way of doing traditional "long multiplication" taught to young students.
Steps-
1. Write the first number as horizontal lines, separating each digit by a bit of space. See the first picture, "13" is horizontal, one line, space, 3 lines.
2. Write the second number in the same way, but vertically.
3. Count the intersections in each diagonal grouping (see the ovals). This represent the digit that goes in each tenths place, with the top left being the largest digit, and the bottom right being smallest. (See the first pic: there is one intersection in the hundred place-→ 100. There are five in the tens place-→ 50. 6 in the ones place-→ 6.)
4. Now simply add the # of intersections, translated into sensible numbers as described in the above parentheses: 100+50+6=156. Multiplication done!

152 x 81

100 x 81 + 10 x 81 x 5 + 81 x 2 = 12,312

100 x 81 = 8100

10 x 81 = 810 x 5 = 4050 (8 x 5 = 40 which 4000. 10 x 5 = 50)

81 x 2 = 162

add

12,312

What the cheese.

Steps-

1. Write the first number as horizontal lines, separating each digit by a bit of space. See the first picture, "13" is horizontal, one line, space, 3 lines.

2. Write the second number in the same way, but vertically.

3. Count the intersections in each diagonal grouping (see the ovals). This represent the digit that goes in each tenths place, with the top left being the largest digit, and the bottom right being smallest. (See the first pic: there is one intersection in the hundred place-→ 100. There are five in the tens place-→ 50. 6 in the ones place-→ 6.)

4. Now simply add the # of intersections, translated into sensible numbers as described in the above parentheses: 100+50+6=156. Multiplication done!