a number is added to 10and12.if the product of the sum obtained is48,find the number

a number is added to 10: x+10

if it's added to 12, that would be x+12

Not sure what the product is supposed to be.
Do you mean (x+10)(x+12) = 48 ?
If so, solve the quadratic, or just note that 6*8 = 48
... also (-8)(-6) = 48