Your vector Height has six elements, with 0 as the first element. Given this, your apparent effort to plot v vs. Height is causing the error because [0; v] and Height need to be the same length. The code below achieves this with test data for v (replace as necessary) The code also sets to length(Height) the number of iterations in the for-loop and the number of subplots (adjust as necessary).
% data given in question (6x1 vector)
Height = [0;3;6;9;12;15];
% test data (replace as needed)
v = rand(length(Height)-1,10);
for i = 1:length(Height)
plot([0; v(:,i)], Height);
ylabel('Height of the structure (m)','FontSize',12);