According to the definition in Article 100, an Equipment Grounding Conductor (EGC) is the conductive path(s) that provides a ground-fault current path and connects normally non–current-carrying metal parts of equipment together and to the system grounded conductor or to the grounding electrode conductor, or both.

Since the EGC does not carry current normally but only carries current under a ground-fault condition (as mentioned in the definition), it is not required to be sized like current carrying conductors. An EGC is sized from NEC^® Table 250.122, based on the size of the overcurrent device protecting the circuit.

In the image, the only overcurrent protection for the conductors connected to the feed through lugs at the bottom of the panelboard is the main 200 amp circuit breaker. According to Table 250.122, what is the minimum size equipment grounding conductor required to bond the gutter box?

For complete code sections, refer to the actual NEC^® text at NFPA.ORG. Once there, click on their link to free access to the 2017 NEC^® edition of NFPA 70.