MySQL count columns on specific value

You can do this using SUM and CASE:

select user_id,
  sum(case when product_id = 1 then 1 else 0 end) as prod_1_count,
  sum(case when product_id = 2 then 1 else 0 end) as prod_2_count,
  sum(case when product_id = 3 then 1 else 0 end) as prod_3_count,
  sum(case when product_id = 4 then 1 else 0 end) as prod_4_count
from your_table
group by user_id