The math behind Chinese Multiplication is actually pretty simple, in the images above show step by step how to lay the math out. The red line is the current step that the picture is guiding you through and the black is past steps. The way this works is the far left side is the single numbers place and as you get farther to the right it starts to turn into the tenths place or the hundreds place ect.
Step 1: Draw the single digit lines
Step 2: Draw the 2nd digit lines
Step 3: Draw the 2nd numbers first digit lines in a cross hatching direction
Step 4: Draw the 2nd numbers 2nd digit lines lower on the line in a cross hatching direction
Step 5: Count far lower right corner's intersections
Step 6: Count the upper left corner's intersections
Step 7: Count the whole middle section's intersection
Step 8: Move the tenths place number to the section on the left until you reach the first section on the right
Step 9: From left to right in that order is the answer to your multiplication question!