1. Stating the problem: Factorise the expression $$-32h^5j^3y^4 + 64h^2j^4y^7$$.\n\n2. Identify the greatest common factor (GCF) for each part:\n- Numerical coefficients: GCF of 32 and 64 is 32.\n- Variable $h$: lowest power is $h^2$.\n- Variable $j$: lowest power is $j^3$.\n- Variable $y$: lowest power is $y^4$.\nSo the GCF is $$32h^2j^3y^4$$.\n\n3. Factor out the GCF from each term:\n$$-32h^5j^3y^4 = -1 \, \times 32h^2j^3y^4 \times h^3$$\n$$64h^2j^4y^7 = 1 \, \times 32h^2j^3y^4 \times 2jy^3$$\n\n4. Write the original expression as:\n$$-32h^5j^3y^4 + 64h^2j^4y^7 = 32h^2j^3y^4 (-h^3 + 2jy^3)$$\n\n5. Final answer:\n$$\boxed{32h^2j^3y^4 ( -h^3 + 2jy^3 )}$$