I wiil do this without a calculator:
$4456 \cdot 4455 = 4455^2+4455 = 4450\cdot4460 + 25 + 4455.$
$4450\cdot4460 = 100\cdot(445\cdot446) = 10\cdot((445^2)+445) = 100*((100*(44\cdot45) + 25) + 445)$
Yay, $44 \cdot 45$ is easy! Everyone knows it's $1980!$ So, $1980\cdot100=198000,$ and plus $25$ yields $198025.$ Next, we add $445$ getting $198470.$ Then times $100$ yields $19847000!$ Now, we can add this to $25$ and $4455,$ easy addition gets $19851480!$ That's your answer, WITHOUT A CALC!