There are multiple ways to do that.
One simple way is reverse the Y-axis direction (assuming the data is originally sorted descendingly) -
x = {'Breast' 'Colorectal' 'Lung\_NonSmallCell' 'Prostate' 'Skin\_Melanoma' 'Pancreas' 'Liver' 'Gastroesophageal' 'Ovarian' 'Kidney\_ClearCell' 'Lymphoid' 'Urothelial' 'CNS\_Medullo' 'CNS\_Glioma' 'Sarcoma\_Other' 'NET\_Pancreas' 'Biliary' 'HeadAndNeck\_Other' 'Uterus' 'Thyroid' 'Sarcoma\_GIST' 'Sarcoma\_Leiomyo' 'Cervix' 'CNS\_PiloAstro' 'NET\_Gastrointestinal' 'Lung\_SmallCell' 'Sarcoma\_Osteo' 'Kidney\_Chromophobe' 'Sarcoma\_Lipo' 'Mesothelium' 'HeadAndNeck\_SalivaryGland' 'Myeloid' 'Kidney\_Papillary' 'NET\_Lung' 'Skin\_Carcinoma'};
updatedStrings = strrep(x, '''', '"');
y = [996 710 588 560 406 347 340 328 284 237 218 200 138 131 131 119 114 91 75 67 67 64 59 58 54 53 44 43 42 41 34 34 32 26 25];
barh(x,y)
width = 1000; % Set the width in pixels
height = 900; % Set the height in pixels
set(gcf, 'Position', [100, 100, width, height]);
%Get the current axes
ax = gca;
%Reverse the y-axis direction
ax.YDir = 'reverse';