Unit's digit in (784)¹²⁶ + (784)¹²⁷ is :

Unit digit of 4² is 6
So, unit digit in (4²)⁶³ is 6
∴ Unit digit of (784)¹²⁶ = Unit digit in 4¹²⁶, which is 6
Unit digit in 4¹²⁷ = Unit digit in (4¹²⁶ × 4) = Unit digit in (6 × 4), which is 4
∴ Unit digit in (784)¹²⁷ is 4
Hence, unit digit of [(784)¹²⁶ + (784)¹²⁷] = Unit digit of (6 + 4) = Unit digit of 10, which is 0