How to name an unsaturated spiro compound with many substituents?
The parent structure is a spiro compound, which has a fixed numbering starting in the smaller ring.
The corresponding actual wording in the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) reads as follows:

P-24.2.1 Monospiro alicyclic ring systems
Mono spiro parent hydrides consisting of two saturated cycloalkane rings are named by placing the nondetachable prefix ‘spiro’ before the name of the unbranched acyclic hydrocarbon with the same total number of skeletal atoms. The number of skeletal atoms linked to the spiro atom in each ring is indicated by arabic numbers separated by a full stop, cited in ascending order and enclosed in square brackets; this descriptor (called in these recommendations the ‘von Baeyer spiro descriptor’) is placed between the spiro prefix and the name of the acyclic alkane. Numbering starts in the smaller ring, if one is smaller, at a ring atom next to the spiro atom and proceeds first around that ring, then through the spiro atom and around the second ring.

In this case, the name of the parent spiro hydrocarbon ring structure is spiro[6.9]hexadecane.
The fixed numbering of the spiro hydrocarbon ring is not modified by the introduction of the double bonds and functional groups. However, low locants must be attributed if there is a choice.

P-14.4 NUMBERING
When several structural features appear in cyclic and acyclic compounds, low locants are assigned to them in the following decreasing order of seniority:
(a) fixed numbering in chains, rings, or ring systems, i.e., when the numbering of a system is fixed, (…), this numbering must be used, both in PINs and in general nomenclature;
(…)
(c) principal characteristic groups and free valences (suffixes);
(…)
(e) saturation/unsaturation:
  (i) low locants are given to hydro/dehydro prefixes (…) and ‘ene’ and ‘yne’ endings;
  (ii) low locants are given first to multiple bonds as a set and then to double bonds (…);
(f) detachable alphabetized prefixes, all considered together in a series of increasing numerical order;
(g) lowest locants for the substituent cited first as a prefix in the name;
(…)

Thus, low locants are first assigned to the principal characteristic group, which is carboxylic acid. This leads to the name spiro[6.9]hexadecane-8,14-dicarboxylic acid.
Next, locants are assigned to the double bonds according to Rule (e), which yields (8​E,11​Z,15​Z)-spiro[6.9]hexadeca-2,8,11,15-tetraene-8,14-dicarboxylic acid.
Finally, locants are assigned to all other substituents. Therefore, the correct name for the complete compound is (8​E,11​Z,15​Z)-4-amino-11-carbamoyl-3-chloro-2-(chlorocarbonyl)-9-cyano-5-formyl-4-hydroxy-13-methoxy-12-(methoxycarbonyl)-10-oxospiro[6.9]hexadeca-2,8,11,15-tetraene-8,14-dicarboxylic acid.