The line draw[help lines,xstep=.1,ystep=.1] (0,0) grid (1,1);, which is of course taken from Drawing on an image with TikZ, nowadays generates an error. I must admit I have not kept up with LaTeX, specifically TikZ, that much. Why does this not work?

Picture of wrong output

Error message

! Arithmetic overflow.

pgf@pathgrid ...de c@pgf@counta byc@pgf@countb 

                                                  relax pgfutil@tempdima =...

l.42 ... lines,xstep=.1,ystep=.1] (0,0) grid (1,1)

                                                  ; %%% --- this is the firs...

I can't carry out that multiplication or division,

since the result is out of range.

MWE for extra-picture.pdf

documentclass[

]{standalone}



usepackage{

    tikz,

}



usepackage{lmodern}

usepackage{microtype}

usepackage[T1]{fontenc}

usepackage[utf8]{inputenc}



begin{document}

begin{tikzpicture}

filldraw[fill=black!50] (0,0) rectangle (4,2);

end{tikzpicture}

end{document}

MWE

documentclass[

fontsize=11pt,

DIV=12,

]{standalone}



usepackage{

    tikz,

}



usetikzlibrary{

    calc,

}



usepackage{lmodern}

usepackage{microtype}

usepackage[T1]{fontenc}

usepackage[utf8]{inputenc}



begin{document}

begin{tikzpicture}[

every node/.style={

    node font=sffamily,

},

month/.style={

    rectangle,

    draw=black,

    very thick,

    fill=black!40,

},

normal/.style={

    draw,

    font=small,

    rectangle,

},

]

node [month, anchor=west] (AAA) at (0,0) {kkkkk};

node [normal, anchor=west] (AAAstuff) at ($(AAA.east)+(1cm,0)$) {Text};



node[anchor=west, inner sep=0] (ENVimage) at ($(AAAstuff.east)+(2cm,0)$) {includegraphics[width=2cm]{extra-picture.pdf}};

begin{scope}[x={(ENVimage.south east)},y={(ENVimage.north west)}]

draw[help lines,xstep=.1,ystep=.1] (0,0) grid (1,1); %%% --- this is the first line that yields the non-working MWE

%draw[help lines,] (0,0) grid (1,1);

%foreach x in {0,1,...,9} { node [anchor=north] at (x/10,0) {0.x}; }

%foreach y in {0,1,...,9} { node [anchor=east] at (0,y/10) {0.y}; }

%node[fill=white] at (0.5,0.5) {111111};

end{scope}



end{tikzpicture}

end{document}

I guess you want something like this.

documentclass[

fontsize=11pt,

DIV=12,

]{standalone}



usepackage{

    tikz,

}



usetikzlibrary{

    calc,

}



usepackage{lmodern}

usepackage{microtype}

usepackage[T1]{fontenc}

usepackage[utf8]{inputenc}



begin{document}

begin{tikzpicture}[

every node/.style={

    node font=sffamily,

},

month/.style={

    rectangle,

    draw=black,

    very thick,

    fill=black!40,

},

normal/.style={

    draw,

    font=small,

    rectangle,

},

]

node [month, anchor=west] (AAA) at (0,0) {kkkkk};

node [normal, anchor=west] (AAAstuff) at ($(AAA.east)+(1cm,0)$) {Text};



node[anchor=west, inner sep=0] (ENVimage) at ($(AAAstuff.east)+(2cm,0)$)

{includegraphics[width=2cm]{example-image-duck.pdf}};

begin{scope}[shift={(ENVimage.south west)},x={(ENVimage.south east)},y={(ENVimage.north west)}]

draw[help lines,xstep=0.1,ystep=0.1] (0,0) grid (1,1); %%% --- this is the first line that yields the non-working MWE

%draw[help lines,] (0,0) grid (1,1);

%foreach x in {0,1,...,9} { node [anchor=north] at (x/10,0) {0.x}; }

%foreach y in {0,1,...,9} { node [anchor=east] at (0,y/10) {0.y}; }

%node[fill=white] at (0.5,0.5) {111111};

end{scope}



end{tikzpicture}

end{document}

I think you used the code that puts a grid on top of an image at the origin, but your image is not at the origin, so I added shift={(ENVimage.south west)} and there is no issue.