How does the cross method ("vertically and crosswise") multiply two 2-digit numbers, e.g. 32 × 21?

Units = product of units; tens = the two cross-products added; hundreds = product of tens — then carry.

For (a b) × (c d): units = b·d, tens = a·d + b·c, hundreds = a·c.

32 × 21 → units 2·1 = 2 → cross 3·1 + 2·2 = 3 + 4 = 7 → hundreds 3·2 = 6 → 672.

Check: 32 × 21 = 672. ✓ It's just the FOIL expansion (10a+b)(10c+d) read place-by-place — the Vedic Urdhva-Tiryagbhyam sutra.