[Solved] Can we call a private procedure of a package from another package and can we call database procedure from a private package

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If by private, you mean a procedure that’s defined in the package body and not exposed in header, then no. The other package won’t be able to “see” the procedure.

SQL> CREATE OR REPLACE PACKAGE foo AS END; -- No "public" procedures/functions
  2  /

Package FOO compiled

SQL> CREATE OR REPLACE PACKAGE BODY foo
  2  AS
  3    PROCEDURE priv IS BEGIN NULL; END; -- "Private" procedure
  4  END;
  5  /

Package Body FOO compiled

SQL> CREATE OR REPLACE PACKAGE other_pkg
  2  AS
  3    PROCEDURE call_priv_proc;
  4  END;
  5  /

Package OTHER_PKG compiled

SQL> CREATE OR REPLACE PACKAGE BODY other_pkg
  2  AS
  3    PROCEDURE call_priv_proc
  4    IS
  5    BEGIN
  6      foo.priv;
  7    END;
  8  END;
  9  /

Package Body OTHER_PKG compiled

LINE/COL  ERROR
--------- -------------------------------------------------------------
6/5       PL/SQL: Statement ignored
6/9       PLS-00302: component 'PRIV' must be declared
Errors: check compiler log

If by database procedure, you mean a standalone procedure not in a package, then yes – provided that the caller has EXECUTE permission on the procedure. Whether the procedure is defined with Invoker’s or Definer’s rights also comes into play. See Invokers and Definers Rights

solved Can we call a private procedure of a package from another package and can we call database procedure from a private package