Steps

Base

1. You just need to know your multiplication tables from 1 to 5 then all the others are easily found on your hands
2. We already have the number 5 represented by the number of fingers on each hand
3. We raise our fingers to complete
4. Each finger raised is worth 10
5. The bent fingers must multiply one by the other

7x7

1. Point to have 7x7, we only raise 2 fingers on each hand
2. We therefore have 4 fingers raised in total, which makes 10+10+10+10=40
3. We have 3 fingers bent on the left hand and 3 on the right hand, which makes 3x3=9
4. We add these two results 40+9=49
5. We obtain the result of the multiplication of 7x7=49

6x8

1. We raise 1 finger on the left hand and 3 on the right hand to have 6x8
2. We therefore have 4 fingers raised in total, which makes 10+10+10+10=40
3. We have 4 fingers bent on the left hand and 2 on the right hand, which makes 4x2=8
4. We add these two results 40+8=48
5. We obtain the result of the multiplication of 6x8=48

9x7

1. We raise 4 fingers on the left hand and 2 on the right hand to have 9x7
2. We therefore have 6 fingers raised in total, which makes 10+10+10+10+10+10=60
3. We have 1 bent finger on the left hand and 3 on the right hand, which makes 1x3=3
4. We add these two results 60+3=63
5. We obtain the result of the multiplication of 9x7=63

6x7

1. We raise 1 finger on the left hand and 2 on the right hand to have 6x7
2. So we have 3 fingers raised in total, which makes 10+10+10=30
3. We have 4 fingers bent on the left hand and 3 on the right hand, which makes 4x3=12
4. We add these two results 30+12=42
5. We obtain the result of the multiplication of 6x7=42

Warning

1. It works for all the multiplications of the tables from 1 to 10 inclusive