<?php

function search_article($name_trening, $name_country, $name_city, $name_date) {
    $sql = "SELECT * FROM table";

    $where = [];
    $args = [];
    if ($name_trening !== null) {
        $where[] = 'name=?';
        $args[] = $name_trening;
    }
    if ($name_country !== null) {
        $where[] = 'country=?';
        $args[] = $name_country;
    }
    if ($name_city !== null) {
        $where[] = 'city=?';
        $args[] = $name_city;
    }
    if ($name_date !== null) {
        $where[] = 'date=?';
        $args[] = $name_date;
    }

    if ($where) {
        $sql .= " WHERE ";
        $sql .= join(' AND ', $where);
    }

    // Заглушка
    db_query($sql, $args);
}

function db_query($sql, $args) {
    echo "Запрос: " . $sql . "\n";
    echo "Аргументы: " . join(', ', $args) . "\n\n";
}

search_article(null, 'b', 'c', 'd');
search_article('a', null, 'c', 'd');
search_article(null, null, null, 'd');
search_article('a', 'b', null, null);
search_article(null, null, null, null);