I really wonder why my method is wrong. Could you explain step-by-step and why my methods wrong. Drawings includes just one time isn't it enough for simplification ?
First boolen expression: $$ F = A'B'C'D' + A'B'C'D + A'B'CD + A'B'CD' + A'BC'D + A'BCD + ABC'D + ABCD + AB'C'D' + AB'C'D + AB'CD + AB'CD' $$
my result: $$ C'D + B'D + AB' + BD $$
Second boolean expression : $$ F = A'B'C'D + A'BC'D' + A'BC'D + A'BCD' + ABC'D' + ABC'D + ABCD' + AB'C'D' + AB'C'D + AB'CD + AB'CD' $$ the other one
my second result: $$ BD' + C'D + AB' $$
You have 12 terms and only 11 1's. You missed the 1st term on second row.
Second Kmap and answer is correct.
Edit... You say: $$F(ABCD) = AB′ + C′D + BC′ + BD′$$ is the correct answer for the second kmap.
Consensus Law says $X Y + X'Z + Y Z = X Y + X'Z$.
So rearranging to make it easier to see: $DC′ + D′B + C′B = DC′ + D′B$.
$BC'$ is redundant.
If you include $BC'$, you must also include $AD'$. It's just as redundant. $$BD′ + B′A + D'A = BD′ + B′A$$
The only correct answer for kmap 2 is: $$F(ABCD) = AB′ + C′D + BD′$$