filtering - Discard Elements of list with given criteria

I have the following list:

{{3506, 0.120908, 
  0.213813, <|1 -> {7, 9, 18, 20}, 6 -> {15}|>}, {3726, 0.119108, 
  0.209133, <|1 -> {6, 8, 9, 13, 18, 20}, 3 -> {15}|>}, {3761, 
  0.116293, 
  0.203036, <|1 -> {6, 8, 14, 18, 20}, 2 -> {12}, 4 -> {15}|>}, {3946,
   0.107619, 
  0.192869, <|3 -> {6}, 1 -> {7, 18, 20}, 2 -> {12}|>}, {4016, 

  0.104384, 
  0.190066, <|1 -> {6, 7, 10, 15, 18, 20}, 6 -> {12}|>}, {4086, 
  0.106909, 
  0.187285, <|5 -> {11, 12}, 4 -> {15}, 1 -> {18, 20}|>}, {4236, 
  0.103937, 
  0.188204, <|1 -> {5, 6, 8, 14, 18, 20}, 5 -> {12}|>}, {4271, 
  0.103541, 
  0.186671, <|1 -> {4, 7, 11, 13, 18, 20}, 5 -> {12}, 
   2 -> {15}|>}, {4421, 0.101325, 
  0.186022, <|2 -> {5, 7}, 1 -> {6, 13, 18, 20}|>}, {4491, 0.101609, 

  0.180121, <|1 -> {4, 6, 7, 15, 18, 20}, 6 -> {11}|>}, {4491, 
  0.100645, 0.184125, <|3 -> {7}, 7 -> {10}, 1 -> {18, 20}|>}, {4526, 
  0.0989646, 
  0.17942, <|1 -> {5, 6, 14, 18, 20}, 2 -> {10}, 7 -> {12}|>}, {4561, 
  0.0945528, 
  0.175016, <|1 -> {5, 18, 20}, 5 -> {11}, 8 -> {12}|>}, {4816, 
  0.0968629, 
  0.172952, <|1 -> {3, 10, 18, 20}, 5 -> {11}, 6 -> {12}, 
   2 -> {14}|>}, {4816, 0.100074, 
  0.171889, <|1 -> {6, 18, 20}, 2 -> {10, 14}, 10 -> {11}|>}, {4851, 

  0.0956618, 0.167787, <|15 -> {11}, 1 -> {12, 14, 18, 20}|>}, {4966, 
  0.0933867, 
  0.173685, <|2 -> {3}, 1 -> {5, 7, 10, 18, 20}, 5 -> {12}|>}, {5001, 
  0.0929784, 
  0.171669, <|1 -> {3, 4, 5, 11, 14, 18, 20}, 7 -> {12}|>}, {5186, 
  0.0923044, 
  0.169445, <|2 -> {4, 5, 11, 12}, 1 -> {6, 18, 20}|>}, {5221, 
  0.0938267, 
  0.16939, <|3 -> {3}, 1 -> {6, 18, 20}, 2 -> {10}, 
   5 -> {12}|>}, {5256, 0.0900446, 

  0.167957, <|3 -> {5}, 5 -> {10, 12}, 1 -> {18, 20}|>}, {5256, 
  0.0953461, 
  0.167948, <|2 -> {4}, 1 -> {5, 13, 14, 15, 18, 20}, 
   7 -> {11}|>}, {5291, 0.0919092, 
  0.164553, <|2 -> {5, 10}, 10 -> {11}, 1 -> {13, 18, 20}|>}, {5441, 
  0.0917546, 
  0.167778, <|1 -> {2, 7, 18, 20}, 3 -> {3, 12}, 2 -> {11}|>}, {5511, 
  0.091757, 
  0.165217, <|1 -> {4, 5, 7, 11, 18, 20}, 10 -> {10}|>}, {5511, 
  0.0931502, 

  0.163884, <|3 -> {4, 13}, 8 -> {11}, 1 -> {18, 20}|>}, {5581, 
  0.0952444, 
  0.163607, <|1 -> {2, 12, 18, 20}, 6 -> {10}, 7 -> {11}, 
   3 -> {13}|>}, {5661, 0.0895339, 
  0.165808, <|1 -> {3, 10, 13, 15, 18, 20}, 5 -> {5}|>}, {5696, 
  0.0878405, 
  0.162595, <|4 -> {3}, 1 -> {4, 11, 18, 20}, 5 -> {12}|>}, {5731, 
  0.0884125, 
  0.162495, <|1 -> {2, 3, 18, 20}, 2 -> {5, 11}, 4 -> {10}, 
   3 -> {12}|>}, {5766, 0.0904722, 

  0.161405, <|1 -> {2, 13, 18, 20}, 2 -> {4, 12}, 5 -> {10}, 
   4 -> {11}|>}, {5766, 0.0921969, 
  0.161218, <|1 -> {3, 4, 6, 11, 18, 20}, 11 -> {10}|>}, {5881, 
  0.0843905, 
  0.161821, <|2 -> {3}, 5 -> {5}, 1 -> {12, 18, 20}|>}, {5916, 
  0.0864502, 
  0.160761, <|1 -> {3, 10, 13, 18, 20}, 2 -> {4, 11}, 
   3 -> {5}|>}, {5951, 0.0879725, 
  0.160539, <|4 -> {3}, 1 -> {5, 13, 18, 20}, 3 -> {10, 12}|>}, {5986,
   0.0892943, 

  0.159927, <|2 -> {3, 5}, 9 -> {10}, 1 -> {15, 18, 20}|>}, {6021, 
  0.0897165, 
  0.158098, <|1 -> {2, 14, 18, 20}, 2 -> {4}, 8 -> {10}, 
   4 -> {11}|>}, {6126, 0.0921288, 
  0.156535, <|20 -> {10}, 2 -> {13}, 1 -> {18, 20}|>}, {6136, 
  0.0837377, 0.157748, <|6 -> {4}, 1 -> {5, 10, 11, 18, 20}|>}, {6206,
   0.0858319, 
  0.157381, <|1 -> {2, 5, 12, 18, 20}, 3 -> {4}, 7 -> {10}|>}, {6206, 
  0.0867804, 
  0.157329, <|2 -> {2, 3}, 1 -> {5, 12, 18, 20}, 3 -> {10}, 

   4 -> {11}|>}, {6206, 0.0872168, 
  0.157297, <|4 -> {3}, 1 -> {5, 12, 14, 18, 20}, 6 -> {10}|>}, {6241,
   0.0862107, 
  0.155018, <|2 -> {3, 4, 11}, 9 -> {10}, 1 -> {18, 20}|>}, {6646, 
  0.085206, 
  0.154682, <|2 -> {2}, 3 -> {3, 10}, 
   1 -> {4, 5, 14, 18, 20}|>}, {6751, 0.0862941, 
  0.152039, <|3 -> {2}, 1 -> {3, 11, 18, 20}, 12 -> {10}|>}}

I would like to discard the rows who's fourth element's sum of the key numbers times the length of the respective value vector is less than 4 and more than 12.

Sorry for the format of the list, but I can't find a way to code-format it.

Answer

Just an alternative:

Select[
    list,
    4 <= Tr @ KeyValueMap[# Length[#2] &, #[[-1]] ] <= 12 &
]