How connect 2 external monitors on a laptop (One VGA, one HDMI)

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I want to expand my desktop to 2 monitors and have 3 monitors total. Do I have to buy something like this?
https://www.monoprice.com/product?p_id=12800&gclid=CjwKCAiAhMLSBRBJEiwAlFrsTuwNdUNSpiodEECLfzKsZ1RX3MAZceAWhkt1w3RQNmWva8eGw_hSfhoCl8EQAvD_BwE

because I tried to just plug them both in at the same time but VGA monitor goes to sleep as soon as I plug in the HDMI monitor.

If I buy the above adapter, will it handle both monitors at the same time?

Can someone suggest me way to accomplish this please?