Letting the Negative Emotion Flow

I am not totally getting what it means to “allow the emotion/feeling” to run through my body before choosing to change the thought and change the feeling.

When I sit down to do a model I almost always go right away to changing the thought (to a neutral or positive believable thought) which in turn changes how I feel about the situation.

What does it actually look like to let anger/discomfort/overwhelm/disappointment etc run its course before moving to a more positive-looking thought? Can you give me a concrete example?