You want an A4 document to reach its reader without a fold, but the proposed envelope is called C4. The matching number does not mean matching dimensions: the sheet and the object carrying it have different jobs.
Specify both the finished document and the complete pack it must fit inside.
A4 is the sheet; C4 is the envelope
Premier Paper's envelope brochure and size guide (PDF, pages 2–3) lists A4 at 210 × 297 mm and C4 at 324 × 229 mm. Its guide pairs flat A4 with C4.
Written in the same portrait orientation, those rectangles are 210 × 297 mm and 229 × 324 mm. Reversing the order of the dimensions turns the rectangle; it does not rename the format.
The original illustration shows the relationship between these nominal sizes. It does not measure the inside of a particular envelope or demonstrate a finished pack fitting inside one.
Describe everything that goes inside
“An A4 document” might mean a single loose sheet, several sheets, a stapled pack or a document accompanied by another item. List the actual contents before treating the format name as the entire requirement.
In a fictional event pack, the organiser might need an unfolded information sheet, a separate reply card and a covering letter. Count all three items in the enclosure brief, even if only one carries the main design.
State whether folding is acceptable. If a particular presentation matters, describe it directly: “The information sheet should arrive flat, with no fold through the illustration.” That is more useful than asking for an unspecified “large envelope”.
Confirm fit and closure for the actual pack
Ask the provider to confirm the proposed envelope against the complete contents, including their thickness and any finishing. Confirm that the pack can be inserted and closed as intended. Nominal flat dimensions alone do not settle those practical questions.
For a business-printing enquiry involving an enclosed document, send the finished page size, contents list, quantities and required date. Identify any envelope already selected and whether a representative pack is available. Envelope availability and suitability still need confirmation for the job.
Source: Premier Paper linked above. The pack and diagrams are illustrative; no envelope fit, stock availability or postal classification was tested or established.