To simplify the given function $f(a, b, c, d) = \sum m(0, 1, 2, 3, 4, 6, 8, 9, 10, 11, 12, 14)$ using a Karnaugh Map (K-map), we need to follow these steps:

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Step 1: Construct the K-map

The K-map for a 4-variable function ($a, b, c, d$) is a 4x4 grid. Each cell corresponds to a minterm number. Here’s the typical layout of the cells:

CD\AB	00	01	11	10
00	0	1	3	2
01	4	5	7	6
11	12	13	15	14
10	8	9	11	10

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Step 2: Mark the minterms in the K-map

Place 1s in the cells corresponding to the minterms $0, 1, 2, 3, 4, 6, 8, 9, 10, 11, 12, 14$. Remaining cells are filled with 0.

CD\AB	00	01	11	10
00	1	1	1	1
01	1	0	0	1
11	1	0	0	1
10	1	1	1	1

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Step 3: Group the 1s into rectangles

1. Group 1 (8-cells): Combine all cells in rows 10 and 00. This group corresponds to $a' + b$ (since $c, d$ vary).
2. Group 2 (4-cells): Combine (6, 14, 10, 2 \ ) .