Answer
$$ g_{xxyz}= 360 x^2y^4z^5 .$$
Work Step by Step
Since $ g(x,y,z)=x^4y^5z^6$, then we have
$$ g_x= 4x^3y^5z^6, \quad g_{xx}= 12x^2y^5z^6 .$$
Then, we have
$$ g_{xxy}= 60x^2y^4z^6, \quad g_{xxyz}= 360 x^2y^4z^5 .$$
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.