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The method for constructing a row that has views with equal heights distributed evenly, based on the height of the tallest view is to use the following steps:

1. Determine the height of the tallest view in the row.

2. Set the height of all views in the row to the same value as the height of the tallest view.

3. Use a layout manager or constraints to evenly distribute the views horizontally within the row.

This can be achieved using various layout managers or constraints, depending on the platform and programming language being used. For example, on Android with Java or Kotlin, the LinearLayout can be used with the weightSum and layout_weight attributes to evenly distribute views within a row with equal heights. On iOS with Swift, the UIStackView can be used with the distribution and alignment properties to achieve the same effect.