We show the \(C^0\) estimate for solutions of Hessian quotient equations on the hyperKähler with torsion manifold without any additional assumption on its hypercomplex structure by a novel use of the cone condition directly. Our proof is based on the elementary properties of the fundamental symmetric functions of hyperhermitian matrices which are developed in parallel with that of real symmetric matrices and hermitian matrices. The difficulty lies in the non-commutativity of the algebra of quaternions.
