You could use a couple of vector selection algorithms from the processing toolbox. First, use 'Select by attribute' to select features in your vector layer with the desired value. Input the layer, the attribute field which contains your values, use the
= operator and supply the value (e.g. 6 in your example).
Then run the tool 'Select by location'. Enter your buffer layer as the layer to Select features from, tick the geometric predicate you wish to use (touches, intersects, are within etc). For the input: 'by comparing to features from' select your vector layer where the features are already selected by attribute value, and tick the check box to use selected features only.