statement given by jemmy : b*b + c*c = (a+b)^2 is incorrect.
initially lets assume that Leon's statement is correct : a*b*c = 12 * c
That means a * b = 12
which means there are following possible values of a & b
a = 6 b = 2 or a = 2 b = 6
or
a = 4 b = 3 or a = 3 b = 4
now take a = 6 and b = 2 then
from Claudy's statement 2*a*b = c + 2*b => c = 20
and on using Thomas's statement : 30*d = 6*b*c => d = 8
and Richard's statement : a+b+c+d = a*a => 6 + 2 + 20 + 8 = 6 * 6 => 36 = 36
only Jemmy's statement : b*b + c*c = (a+b)^2 is not satisfying this values.
so jemmy's statement is incorrect.