Vedic Mathematics is a great gift to the modern world from our ancient sages. It is based on 16 sutras (formulae) and 13 upasutras (sub-formulae). The methods are simple, short and speedy. The answers can be worked out in 2 or 3 lines and are computed mentally without using pen and paper. Addition, subtraction, multiplication, etc. can be done from left to right as against traditional right to left. The general multiplication method is easily reversed to allow one-line divisions and the simple squaring method can be reversed to give one-line square roots. The techniques are well tested by scientists and engineers at NASA and are being taught globally.
VERTICALLY & CROSSWISE
Lets apply one of the 16 Sutras here to find the product of 78 x 36. The sutra says ‘ūrdhva tiryagbhyāṃ’ meaning vertically and crosswise.
We write the numbers one above the other, aligning place values as in the usual method of multi-digit multiplication.
The ones place of the product is determined vertically, by computing 6×8. The result, 48, tells us the one’s place of the product is an 8, and we have an additional 4 tens to keep track of.
The tens place of the product is determined crosswise, by taking both the product 6×7 and also the product 3×8, plus the extra 4 tens we have from above. This yields 42+24+4=70 tens, so the tens place of the product is 0, and we have an additional 7 hundred to keep track of.
Finally, the hundreds place of the product is determined vertically, by computing 3×7, plus the 7 extra hundreds from above. That gives 21+7=28 hundred.
Putting it all together, we have 2808 as the product.
Let us apply the method on a bigger value, say 978 x 423
Ones place: 3×8=24; write down 4, remember 2. 
Tens place: 2 + 3×7 + 2×8 = 39; write down 9, remember 3. 
Hundreds place: 3+3×9+2×7+4×8=76; write down, 6, remember 7. 
Thousands: 7+2×9+4×7=53; write down 3, remember 5. 
Ten-thousands: 5+4×9=41; write down 41. 
Putting it all together, we have 413694 as the product.
Try it and let me know how you like it!