幅 and 奥行き: width from the front and depth from front to back
Read furniture’s side-to-side width separately from its front-to-back depth when checking the space available for placement.
Side-to-side width from the front
幅, read はば, names width. 正面から棚の幅を測りました。 says that the shelf’s width was measured using the front as the reference.
入口の幅より広い家具は、そのままでは通せません。 says that furniture wider than the entrance cannot pass through as it is. Preserve the condition そのままでは.
Depth from front to back
奥行き, read おくゆき, names front-to-back depth. この机は奥行きが浅いです。 says that this desk has a shallow depth.
収納場所の奥行きを確認してください。 asks someone to check the depth of the storage space. It is not a request to measure its height.
Matching dimensions to available space
幅は十分ですが、奥行きが足りません。 says that the width is sufficient but the front-to-back space is insufficient. Identify the direction in which space is lacking.
棚の奥行きは、取っ手を含めると変わります。 says that including the handle changes the measured depth of the shelf. Check whether measurements use the same boundary.
Does 収納場所の奥行きが足りません。 say that the storage space is too low?
Show the answer and why
No. It says that front-to-back space is insufficient. Height requires a separate assessment.