The reason why this is an Modern style is because the serifs are completely angled from the font. There is no curve in it for it to be lets say a old style or a transitional. Through the strokes of each letter is most of the time squared off.

The reason why this is a slab serif is because each bracket are very bulky and the strokes of he font are very thick also.

The reason why this font is a san serif because the font does not contain any serifs.

I think the reason that this would be Old Style is because that strokes are a lot thicker than old style and the brackets on the corners of the H are more angled looking other than Transition which have more of a curve to its brackets.

The reason why I think this would be Transitional because the strokes are a lot thinner than transitional and brackets look more sculpted than the Old style.