Make Andy the same number of units in both ratios: A:F = 3:4 = 12:16, A:M = 4:5 = 12:15. So A : M : F = 12 : 15 : 16. Mother − Andy = 3u = 33 cm.

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• Andy : Father = 3 : 4 = 12 : 16
• Andy : Mother = 4 : 5 = 12 : 15
• Andy : Mother : Father = 12 : 15 : 16
• Mother − Andy = 15u − 12u = 3u → 33 cm
• 1 unit → 33 ÷ 3 = 11 cm; Father → 16 × 11 = 176 cm

His father's height is 176 cm.
Check: Mother = 15 × 11 = 165 cm, Andy = 12 × 11 = 132 cm; 165 − 132 = 33, 132:176 = 3:4, 132:165 = 4:5. ✓