A rigid constitution is one that has a special, formal amendment procedure explicitly laid down within the constitution itself. This procedure typically requires more than a simple majority of the legislature - it may demand a two-thirds or three-quarters supermajority, approval by a specified number of state legislatures, or a national referendum before any change can take effect.
The defining feature of a rigid constitution is that the process for altering it is deliberately made difficult and is prescribed within the document. The Nigerian Constitution, for example, is rigid: Section 9 specifies that amendments require approval by a two-thirds majority of both chambers of the National Assembly and ratification by at least two-thirds of all state Houses of Assembly.
A flexible constitution, by contrast, can be amended through the ordinary legislative process - no special procedure is required. An unwritten constitution is not codified in a single document and typically relies on conventions, statutes, and judicial precedents. A democratic constitution relates to the system of government rather than to the amendment procedure.
When a question refers to amendment procedures being "enshrined" in the constitution, it points directly to a rigid constitution, because that formality and specificity is what distinguishes it from other types.