To compare the distributions of two histograms, you should examine several key characteristics: their shapes, centers, spreads, and any outliers.

First, let’s analyze the shapes of the histograms. Observe the overall form of each histogram. Are they symmetrical, skewed to the left or right, or do they exhibit multiple peaks? The shape provides valuable insights into the nature of the data. For instance, a symmetrical shape suggests a normal distribution, whereas a skewed shape indicates that the data is unevenly distributed.

Next, focus on the centers of the histograms. The center represents the point where most data points are concentrated, which can typically be identified by the tallest bars in each histogram. If one histogram has its tallest bars positioned further to the right, this indicates that its data values are generally higher. You can quantify these differences by comparing the mean or median of each dataset.

The spread of the histograms is another crucial aspect to consider. The spread indicates the variability of the data. A wider spread suggests that the data points are more dispersed, while a narrower spread indicates that they are clustered more closely together. You can compare the range, which is the difference between the highest and lowest values, or the interquartile range (IQR), which represents the range of the middle $50\%$ of the data, for each histogram.

Lastly, be on the lookout for outliers—data points that significantly deviate from the rest of the data. Outliers can heavily influence the overall interpretation of the dataset, so it is essential to note if one histogram has more outliers than the other.

By carefully examining these aspects, you can effectively compare the distributions of two histograms.