Warning: standard form when not qualified and applied to a linear relation usually means #color(blue)("linear standard form") # which is #Ax+By=C# with #A,B,C in ZZ, and A >= 0#
However this question was asked under "Polynomials in Standard Form", so I have assumed you want something of the form:
#color(white)("XXX")color(red)(y= "polynomial standard form expression")#
A #color(red)("polynomial standard form expression")# arranges the variable terms (typically with #x# used as the variable) win descending sequence of exponents: #color(red)(a_nx^n+a_(n-1)x^(n-1)+...+a_2x^2+a_1x^1+a_0x^0)#
Given
#color(white)("XXX")y-6=4(x+3)#
we can expand the right side:
#color(white)("XXX")y-6 = 4x+12#
then adding #6# to both sides:
#color(white)("XXX")y=color(red)(4x+18)#
It would be unusual, but you could write this to make the #color(red)("polynomial standard form")# explicit:
#color(white)("XXX")y=color(red)(4 * x^1+18 * x^0)#
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Without going into the details of derivation, if you wanted the #color(blue)(" linear standard form")# is would be
#color(white)("XXX")color(blue)(4x-y=-18)#
