Numerically greatest coefficient in a multinomial expression

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Given the expression $E=(1+3x+8x^2)^{12}$ . I was trying to find the numerically greatest coefficient of any power of x in the above expression.

My try

I wrote the general coefficient as

$(10)! (3^p)(8^q)/{(p!)(q!)(10-p-q)!} $ However I am unable to maximise this expression. I was hoping for some hints or an alternate solution ?