So I’m trying to connect my dropper and hopper so that my hopper will accept something then at the same time, my dropper will drop something when I place that item in the hopper.
You're probably going to want to hook up a pulse circuit to both (by placing a sticky piston in the ground, placing a redstone block on top, and then placing a piece of redstone on the ground next to the sticky piston, or (this is a separate solution) you can use a comparator next to the hopper, and then hook a repeater up, and attach the redstone lines to both.
How about you put your hopper on the dropper, place a comparator facing the hopper, and wire up the comparator to the dropper? If that doesn't work, then follow this blueprint:
The 1 is redstone dust, the 2 is the comparator facing 3, which is a hopper pointed to 4, a dropper. And finally, 5 is a repeater facing right. This is a bird's eye view. Hope it works!
The name of the circuit you're looking for is "auto-dropper". There are generally two types in most common use:
This is the most compact one, utilizing quasi-connectivity both to power the piston to assemble an observer clock, and to trigger the dropper. It's operating at double hopperspeed (can keep up with being fed from two hoppers at once), quite lag-friendly (no use of redstone dust), 1-tileable, can be faced in any direction and fed from 5 out of 6 sides. It has the disadvantage that being fed slower than that it's exceptionally noisy, and more expensive in materials than the alternatives.
The other design utilizes the comparator in subtract mode both to read contents of the dropper and to provide the comparator clock functionality. The variants differ in compactness, speed, and item overhead (some drop the item as soon as it arrives, some only start after a certain number (41 64-stackable or 10 16-stackable) items accumulated.
Variant A (nearest) is probably the oldest, and most popular - single hopper speed, powering the dropper through a block over the comparator, a separate path from the power to trigger the comparator clock.
Variants B 1,2,3 (second row) differ in footprint, and utilize same-path signal to trigger both the comparator and the dropper, but are otherwise equivalent to A.
Variants C (in the back, again, 1 and 2 differ in cost and footprint) are more compact, operate at double hopperspeed but only activate after being partially filled.